Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed MF or SS, stages IIB to
             IVB with measurable disease and/or detectable blood involvement based on the Global
             Cutaneous Lymphoma Response Criteria

          -  Patients must have had at least one line of prior systemic therapy

          -  Age >= 18 years. Because no dosing or adverse event data are currently available on
             the use of duvelisib in combination with nivolumab in patients < 18 years of age,
             children are excluded from this study

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 50%)

          -  Absolute neutrophil count >= 1000/mcL

          -  Platelets > 75,000/mcL

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) or =< 5 x
             institutional ULN if with history of Gilbert's syndrome

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x institutional ULN

          -  Creatinine =< 2.0 x institutional ULN

          -  Patients with treated brain metastases are eligible if follow-up brain imaging after
             central nervous system (CNS)-directed therapy shows no evidence of progression

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class 2B or better

          -  The effects of nivolumab and duvelisib on the developing human fetus are unknown. For
             this reason and because other therapeutic agents used in this trial are known to be
             teratogenic, women of child-bearing potential (WOCBP) and men must agree to use
             adequate contraception (hormonal or barrier method of birth control; abstinence) prior
             to study entry and for the duration of study participation. WOCBP should use an
             adequate method to avoid pregnancy for 5 months after the last dose of investigational
             drug. WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25
             IU/L or equivalent units of human chorionic gonadotropin [HCG]) within 7 days prior to
             the start of nivolumab. Women must not be breastfeeding. Men who are sexually active
             with WOCBP must use any contraceptive method with a failure rate of less than 1% per
             year. Men receiving nivolumab and duvelisib and who are sexually active with WOCBP
             will be instructed to adhere to contraception for a period of 7 months after the last
             dose of investigational product. Women who are not of childbearing potential (i.e.,
             who are postmenopausal or surgically sterile as well as azoospermic men) do not
             require contraception. WOCBP is defined as any female who has experienced menarche and
             who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy)
             or who is not postmenopausal. Menopause is defined clinically as 12 months of
             amenorrhea in a woman over 45 in the absence of other biological or physiological
             causes. In addition, women under the age of 55 must have a documented serum follicle
             stimulating hormone (FSH) level less than 40 mIU/mL

          -  Should a woman become pregnant or suspect she is pregnant while she or her partner is
             participating in this study, she should inform her treating physician immediately. Men
             treated or enrolled on this protocol must also agree to use adequate contraception
             prior to the study, for the duration of study participation, and 7 months after
             completion of administration of investigational agents on this study

          -  Ability to understand and the willingness to sign a written informed consent document.
             Participants with impaired decision-making capacity (IDMC) who have a
             legally-authorized representative (LAR) and/or family member available will also be
             eligible

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

        Exclusion Criteria:

          -  Prior therapy with a PI3K inhibitor

          -  Prior therapy with nivolumab or other agents targeting T-cell co-stimulation or
             checkpoint pathways

          -  Patients with active autoimmune disease or history of autoimmune disease that might
             recur, which may affect vital organ function or require immune suppressive treatment
             including systemic corticosteroids, should be excluded. These include but are not
             limited to patients with a history of immune related neurologic disease, multiple
             sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia
             gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE),
             connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's,
             ulcerative colitis, hepatitis; and patients with a history of toxic epidermal
             necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be
             excluded because of the risk of recurrence or exacerbation of disease. Patients with
             vitiligo, endocrine deficiencies including thyroiditis managed with replacement
             hormones including physiologic corticosteroids are eligible. Patients with rheumatoid
             arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with
             topical medication and patients with positive serology, such as antinuclear antibodies
             (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ
             involvement and potential need for systemic treatment but should otherwise be eligible

          -  Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus,
             residual hypothyroidism due to autoimmune condition only requiring hormone
             replacement, psoriasis not requiring systemic treatment, or conditions not expected to
             recur in the absence of an external trigger (precipitating event)

          -  Patients should be excluded if they have a condition requiring systemic treatment with
             either corticosteroids (> 10 mg daily prednisone equivalents) or other
             immunosuppressive medications within 14 days of study drug administration. Inhaled or
             topical steroids and adrenal replacement doses < 10 mg daily prednisone equivalents
             are permitted in the absence of active autoimmune disease. Patients are permitted to
             use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids
             (with minimal systemic absorption). Physiologic replacement doses of systemic
             corticosteroids are permitted, even if < 10 mg/day prednisone equivalents. A brief
             course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for
             treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction
             caused by contact allergen) is permitted

          -  History of tuberculosis treatment within the 2 years prior to enrollment

          -  Ongoing treatment with other immunosuppressive agent including, but not limited to,
             methotrexate, azathioprine, anti-tumor necrosis factor (TNF) agents, etc. with the
             exception of steroids

          -  Administration of a live or live attenuated vaccine within 6 weeks of initiation of
             study therapy

          -  Ongoing treatment with systemic steroids at dose equivalent to greater than prednisone
             10 mg daily or other immunosuppressive medication within 7 days of initiation of study
             therapy

               -  Inhaled steroids will be permitted

               -  Topical steroids for cutaneous manifestations of MF/SS will be permitted

               -  Patients prescribed prednisone 10 mg PO daily or less (or equivalent) will not be
                  excluded, provided they have been on a stable dose for at least 4 weeks prior to
                  enrollment

          -  Concomitant use of another systemic therapy for MF/SS. Patients must have the
             following minimum wash-out from previous treatments:

               -  At least 8 weeks for low-dose (12 Gy or less) total skin electron beam therapy
                  (TSEBT)

               -  At least 4 weeks for systemic cytotoxic anticancer agents or for tumor-targeting
                  monoclonal antibodies (mAbs), with the exception of alemtuzumab, for which the
                  washout is at least 16 weeks

               -  At least 2 weeks or 5 half-lives for systemic retinoids, interferons, vorinostat,
                  romidepsin, and denileukin diftitox, or anticancer investigational agents that
                  are not defined as immunotherapy

               -  At least 2 weeks for local radiation therapy

               -  At least 1 week for topical retinoids, nitrogen mustard, or imiquimod Continued
                  use of select concomitant topical steroids is permitted if the patient has
                  remained clinically stable for at least 4 weeks

               -  Patients who are on low or moderate potency topical corticosteroids may
                  participate if they are on a stable dose for at least 4 weeks before enrollment.
                  Local injections of corticosteroids are acceptable; all corticosteroids will be
                  reported as concomitant medications

          -  Concomitant malignancy requiring active systemic therapy, excluding adjuvant endocrine
             therapy with the following exceptions:

               -  Patients with non-melanoma skin cancer or carcinoma in situ of the cervix will
                  not be excluded

               -  Adjuvant or maintenance therapy to reduce the risk of recurrence of another
                  malignancy (excluding cutaneous T-cell lymphoma) is permissible after discussion
                  with the Washington University principal investigator

               -  Subjects with previous malignancies are eligible if disease-free for > 2 years

          -  History of solid organ transplantation or allogeneic bone marrow transplantation

          -  Uncontrolled infection requiring systemic antimicrobials: Patients on antibacterial,
             antifungal, and antiviral prophylaxis will not be excluded if all other exclusion /
             inclusion criteria are met

          -  Patients with active Epstein-Barr virus (EBV) unrelated to underlying lymphoma
             (positive serology for anti-EBV virus capsid antibody [VCA] immunoglobulin M (IgM)
             antibody and negative for anti-EBV Epstein-Barr nuclear antigen [EBNA] IgG antibody,
             or clinical manifestations and positive EBV polymerase chain reaction [PCR] consistent
             with active EBV infection)

          -  Patients with active cytomegalovirus (CMV) (positive serology for anti-CMV IgM
             antibody and negative for anti-CMV IgG antibody or positive CMV PCR with clinical
             manifestations consistent with active CMV infection) and requiring therapy will be
             excluded from participation in the study. Carriers will be monitored per institutional
             guidelines

          -  Patients should be excluded if they have known active hepatitis B (e.g. hepatitis B
             virus [HBV] surface antigen [HBsAg] reactive) or hepatitis C (e.g. hepatitis C virus
             [HCV] ribonucleic acid [RNA] [qualitative] is detected)

               -  Patients with chronic HBV or HCV are defined as patients with positive hepatitis
                  B serology: Patients with a negative HBsAg and a positive hepatitis B core
                  antibody (HBcAb) require an undetectable/negative hepatitis B deoxyribonucleic
                  acid (DNA) test (e.g. polymerase chain reaction [PCR] test) to be enrolled, and
                  will require prophylactic antiviral treatment initiated prior to the first dose
                  of study drug, and continued until approximately 6 to 12 months after completion
                  of study drug(s)

          -  Patients who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities > grade 1), with the exception of alopecia and
             neuropathy

          -  Patients who are receiving any other investigational agents

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to duvelisib or nivolumab

          -  Patients receiving any medications or substances that are strong inhibitors or
             inducers of CYP3A4 are ineligible to start study therapy. Patients who are on strong
             inhibitors or inducers of CYP3A4 may start study therapy if discontinued 5 half lives
             before start of study therapy. Because the lists of these agents are constantly
             changing, it is important to regularly consult a frequently-updated medical reference.
             As part of the enrollment/informed consent procedures, the patient will be counseled
             on the risk of interactions with other agents, and what to do if new medications need
             to be prescribed or if the patient is considering a new over-the-counter medicine or
             herbal product

          -  Patients with uncontrolled intercurrent illness including, but not limited to, ongoing
             or active infection, interstitial lung disease or active, non-infectious pneumonitis,
             congestive heart failure New York Heart Association (NYHA) grade >= 3, unstable angina
             pectoris, and cardiac arrhythmia

          -  Patients with psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Baseline left ventricular ejection fraction (LVEF) < 45%

          -  Baseline QT interval corrected with Fridericia's method (QTcF) > 500 ms

               -  Note: Criteria does not apply to subjects with a right or left bundle branch
                  block

          -  Pregnant women are excluded from this study because nivolumab has the potential for
             teratogenic or abortifacient effects. Because there is an unknown but potential risk
             for adverse events in nursing infants secondary to treatment of the mother with
             nivolumab, breastfeeding should be discontinued if the mother is treated with
             nivolumab. These potential risks may also apply to other agents used in this study

          -  Patients who have had evidence of active or acute diverticulitis, intra-abdominal
             abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are
             known risk factors for bowel perforation should be evaluated for the potential need
             for additional treatment before coming on study