Inclusion Criteria:

          -  Histologically or cytologically confirmed relapsed or refractory follicular CD30+
             non-Hodgkin lymphoma (NHL) (included in this category are follicular grade I, II,
             IIIa). CD30 positivity > 1% (tumor cells or surrounding peripheral microenvironment)

          -  Patients must have measurable disease by computed tomography (CT) or positron emission
             tomography (PET) scan, with one or more sites of disease >= 1.5 cm in longest
             dimension

          -  Relapsed or refractory disease after at least 1 prior regimen, defined using the 2014
             Lugano classification

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Life expectancy of greater than 3 months

          -  Leukocytes >= 2,500/mcL

          -  Absolute neutrophil count >= 1,000/mcL

          -  Platelets >= 50,000/mcL

          -  Hemoglobin >= 8 g/dL

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (however, patients
             with known Gilbert disease who have serum bilirubin level =< 3 x ULN may be enrolled)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x ULN (AST and/or ALT =< 5 x ULN for patients with liver involvement)

          -  Alkaline phosphatase =< 2.5 x ULN (=< 5 x ULN for patients with documented liver
             involvement or bone metastases)

          -  Creatinine clearance >= 30 mL/min/1.73 m^2 by Cockcroft-Gault

          -  Institutional normalized ratio (INR) and partial thromboplastin time (aPTT) =< 1.5 x
             ULN (This applies only to patients who do not receive therapeutic anticoagulation;
             patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin
             or warfarin, should be on a stable dose.)

          -  Administration of bendamustine or brentuximab vedotin may have an adverse effect on
             pregnancy and poses a risk to the human fetus, including embryo-lethality. Women of
             child-bearing potential and men must agree to use adequate contraception (hormonal or
             barrier method of birth control; abstinence) prior to study entry, for the duration of
             study participation, and for 5 months (150 days) after the last dose of study agent.
             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

          -  Ability to understand and the willingness to sign a written informed consent document

          -  Patients positive for human immunodeficiency virus (HIV) are allowed on study, but
             HIV-positive patients must have:

               -  A stable regimen of highly active anti-retroviral therapy (HAART)

               -  No requirement for concurrent antibiotics or antifungal agents for the prevention
                  of opportunistic infections

               -  A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard
                  polymerase chain reaction (PCR)-based tests

        Exclusion Criteria:

          -  Patients who have had chemotherapy, or radiotherapy within 2 weeks (6 weeks for
             nitrosoureas or mitomycin C, steroid treatment for follicular lymphoma is allowed per
             protocol) prior to entering the study or those who have not recovered from adverse
             events (other than alopecia) due to agents administered more than 2 weeks earlier.
             Specifically, the following therapies are not allowed:

               -  Herbal therapy (1 week washout required)

               -  Treatment with any other investigational agent within 3 weeks prior to cycle 1,
                  day 1.

               -  Prior therapy with bendamustine or a bendamustine-containing regimens with
                  progression within 6 months of receiving treatment

          -  Current or prior use of immunosuppressive medications (including, but not limited to,
             prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor
             necrosis factor [anti-TNF] agents) within 14 days prior to first dose (cycle 1, day
             1). The following are exceptions to this criterion:

               -  Intranasal, inhaled, topical or local steroid injections (e.g., intra-articular
                  injection); steroids as premedication for hypersensitivity reactions; systemic
                  corticosteroid at physiologic doses not to exceed 10 mg/day of prednisone or
                  equivalent may be enrolled

               -  Patients who have received acute, low dose, systemic immunosuppressant
                  medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled

               -  The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone)
                  for patients with orthostatic hypotension or adrenocortical insufficiency is
                  allowed

               -  Patients taking bisphosphonate therapy for symptomatic hypercalcemia. Use of
                  bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis)
                  is allowed

          -  Patients with known uncontrolled central nervous system (CNS) involvement by lymphoma,
             including leptomeningeal involvement

          -  History of hypersensitivity to bendamustine or brentuximab vedotin or any excipient

          -  Known hypersensitivity to Chinese hamster ovary cell products or other recombinant
             human antibodies

          -  History of severe allergic, anaphylactic, or other hypersensitivity reactions to
             chimeric or humanized antibodies or fusion proteins

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to other agents used in study

          -  Known clinically significant liver disease, including active viral, alcoholic, or
             other hepatitis; cirrhosis; fatty liver; and inherited liver disease.

               -  Patients with past or resolved hepatitis B infection (defined as having a
                  negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc
                  [antibody to hepatitis B core antigen] antibody test) are eligible.

               -  Patients positive for hepatitis C virus (HCV) antibody are eligible only if
                  polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)

          -  Neuropathy grade > 1

          -  Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with
             dermatologic manifestations only (e.g., patients with psoriatic arthritis would be
             excluded) are permitted provided that they meet the following conditions:

               -  Rash must cover less than 10% of body surface area (BSA)

               -  Disease is well controlled at baseline and only requiring low potency topical
                  steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone
                  0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)

               -  No acute exacerbations of underlying condition within the last 12 months (not
                  requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate, retinoids,
                  biologic agents, oral calcineurin inhibitors; high potency or oral steroids)

          -  Patients with known active tuberculosis (TB) are excluded

          -  Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited
             to, hospitalization for complications of infection, bacteremia, or severe pneumonia

          -  Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1

          -  Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1.
             Patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract
             infection or chronic obstructive pulmonary disease) are eligible

          -  Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of
             need for a major surgical procedure during the course of the study

          -  Influenza vaccination should be given during influenza season only (approximately
             October to March). Patients must not receive live, attenuated influenza vaccine within
             4 weeks prior to cycle 1, day 1 or at any time during the study

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements