Inclusion Criteria:

          -  Participant is able to understand and willing to sign a written informed consent
             document

          -  Participants must have histologically or cytologically confirmed cutaneous Kaposi
             sarcoma. Participants must have measurable disease with a minimum of five
             bi-dimensionally measurable KS cutaneous marker lesions. If fewer than five
             bi-dimensionally measurable marker lesions are available, the total surface area of
             the marker lesion(s) must be >= 700 mm^2

          -  Participants must have documentation of HIV status

               -  If HIV negative, documentation of a negative HIV rapid test within 21 days before
                  enrollment

               -  If HIV positive, documentation of HIV-1 infection by means of any one of the
                  following:

                    -  Documentation of HIV diagnosis in the medical record by a licensed health
                       care provider

                    -  Documentation of receipt of antiretroviral therapy (ART) (at least two
                       different medications that do not constitute a prescription for pre-exposure
                       prophylaxis [PrEP]) by a licensed health care provider. Documentation may be
                       a record of an ART prescription in the participant's medical record, a
                       written prescription in the name of the participant for ART, or pill bottles
                       for ART with a label showing the participant's name

                    -  Any licensed HIV screening antibody and/or HIV antibody/antigen combination
                       assay confirmed by a second licensed HIV assay such as a HIV-1 Western blot
                       confirmation or HIV rapid multispot antibody differentiation assay

               -  Note: The term "licensed" refers to a kit that has been certified or licensed by
                  an oversight body within the participating country and validated internally
                  (e.g., United States [U.S.] Food and Drug Administration [FDA])

               -  WHO (World Health Organization) and CDC (Centers for Disease Control and
                  Prevention) guidelines mandate that confirmation of the initial test result must
                  use a test that is different from the one used for the initial assessment. A
                  reactive initial rapid test should be confirmed by either another type of rapid
                  assay or an enzyme (E)/carbon immunoassay (CIA) that is based on a different
                  antigen preparation and/or different test principle (e.g., indirect versus
                  competitive), or a Western blot or a plasma HIV-1 ribonucleic acid (RNA) viral
                  load

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1

          -  Life expectancy of greater than 6 months

          -  Hemoglobin >= 8 g/dL (within 7 days before enrollment)

          -  Absolute neutrophil count (ANC): >= 1,000/mm^3 (within 7 days before enrollment)

          -  Platelets: >= 75,000/mm^3 (within 7 days before enrollment)

          -  Bilirubin =< 1.5: x upper limit of normal (ULN) unless the patient is receiving an ART
             drug known to be associated with increased bilirubin, in which case the direct
             fraction should be =< 2 x ULN (within 7 days before enrollment)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional ULN (within 7 days before enrollment)

          -  Serum creatinine =< 2.0 mg/dL/176.8 umol/L; or estimated creatinine clearance >= 15
             mL/minute (1.00 mL/s) (as calculated per the Cockcroft-Gault equation (within 7 days
             before enrollment)

          -  Females of childbearing potential (FCBP, defined as a sexually mature woman who: 1)
             has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been
             naturally postmenopausal for at least 24 consecutive months, i.e., has had menses at
             any time in the preceding 24 consecutive months) must have a negative serum or urine
             pregnancy test with a sensitivity of at least 25 mIU/mL within 10-14 days prior to and
             again within 24 hours of starting pomalidomide and must either commit to continued
             abstinence from heterosexual intercourse or begin TWO acceptable methods of birth
             control, one highly effective method and one additional effective method AT THE SAME
             TIME, at least 28 days before she starts taking pomalidomide. FCBP must also agree to
             ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact
             with a FCBP even if they have had a vasectomy. All patients must be counseled at a
             minimum of every 28 days about pregnancy precautions and risks of fetal exposure

          -  HIV positive participants must be taking stable ART for >= 12 weeks, and have an
             undetectable HIV viral load within 28 days before enrollment. Minor fluctuations up to
             200 copies/mL are acceptable

          -  HIV positive participants must not show recent improvement on ART that may confound
             response evaluation, within the following parameters:

               -  If on ART 12 to 24 weeks, participants must show evidence of KS progression
                  requiring further systemic treatment

                    -  Evidence of KS progression for eligibility include: Any new lesion(s);
                       spreading of lesions by any measurable degree; development of ulceration;
                       worsening edema documented by circumferential measure of limb or body;
                       increase in symptoms such as pain, including negative psychological impact,
                       requiring; any degree disease worsening by imagining) that would prompt
                       expert assessment to recommend further systemic treatment without delay

               -  If on ART for > 24 weeks, must show no evidence of regression in last 8 weeks

                    -  Evidence of KS regression for eligibility include: Measures of edema, lesion
                       size or number, resolution of ulceration, or 20% improvement by imaging in
                       largest diameter. For purposes of this assessment, if there is 20% reduction
                       in size of any lesion, disappearance of any lesion, this constitutes
                       regression unless there is concomitant increase in size or appearance of new
                       lesions elsewhere

          -  Participants must agree to participate in and comply with the mandatory POMALYST Risk
             Evaluation and Mitigation Strategy (REMS) program

          -  Participants must be able to take aspirin 81 mg daily as prophylactic anticoagulation
             (patients intolerant to acetylsalicylic acid (ASA), may use warfarin or low molecular
             weight heparin)

          -  For participants with impaired decision-making capacity (IDMC): Participants with IDMC
             may be eligible for the study provided all other eligibility criteria are satisfied:

               -  The participant's legally authorized representative (LAR) is able and willing to
                  sign consent in addition to the study candidate

               -  Both participant and LAR agree to follow study parameters and ensure that drug is
                  taken per protocol, recorded in the study drug diary, and returned to clinic with
                  any unused pills

        Exclusion Criteria:

          -  Participant who is receiving any other investigational agents

          -  Participant has symptomatic visceral KS involving the lungs or gastrointestinal (GI)
             tract that requires immediate chemotherapy or radiotherapy. Participants with
             minimally symptomatic visceral disease not requiring immediate tumor shrinkage are
             eligible if in provider judgment potential disease progression will not cause a hazard
             for the participant

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

          -  Use of agents containing zidovudine (including Combivir and Trizivir) are prohibited.
             Changes to ART therapy during the study may be made if medically necessary (toxicity,
             failure of regimen, etc.). Use of medications or substances that are strong inhibitors
             of CYP1A2, which include amiodarone, cimetidine, fluoroquinolones (e.g.,
             ciprofloxacin, enoxacin), fluvoxamine, and ticlopidine is prohibited.
             Co-administration of efavirenz, an inhibitor of CYP1A2, with strong inhibitors of
             CYP3A4 and P-glycoprotein (P-gp) is prohibited. Use of erythropoietin is prohibited.
             Co-administration of corticosteroids greater than doses required for treatment of
             adrenal insufficiency is prohibited. Because the lists of these agents are constantly
             changing, it is important to regularly consult frequently-updated list; medical
             reference texts such as the Physicians' Desk Reference may also provide this
             information. As part of the informed consent/enrollment procedures, the participant
             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 participant is considering a new
             over-the-counter medicine or herbal product

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection for which the participants have not completed at least 14 days of therapy
             prior to study enrollment and/or is not clinically stable

          -  Participant has symptomatic congestive heart failure; unstable angina pectoris;
             cardiac arrhythmia; or psychiatric illness/social situations that, in the opinion of
             the investigator, would limit compliance with study requirements

          -  Pregnant women are excluded from this study because pomalidomide is a thalidomide
             analogue with 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 pomalidomide, breastfeeding should be discontinued if the
             mother is treated with pomalidomide

          -  Participants who have had chemotherapy, radiotherapy, or therapies to target KS
             lesions within 4 weeks (6 weeks for nitrosoureas or mitomycin C) with the exception of
             ART, before enrollment

          -  Participants with high clinical suspicion of concurrent Castleman disease or IL-6
             related inflammatory disease

               -  For a reference of signs and symptoms consistent with IL-6 related inflammatory
                  disease or KSHV inflammatory cytokine syndrome (KICS) can refer to publication
                  from Polizzotto Minnesota (MN), et al. Clinical Features and Outcomes of Patients
                  with Symptomatic Kaposi Sarcoma Herpesvirus (KSHV)-associated Inflammation:
                  Prospective Characterization of KSHV Inflammatory Cytokine Syndrome (KICS).
                  Clinical Infectious Diseases, 2016. 62(6):730-8

          -  Participants with a history of malignant tumors other than KS, unless:

               -  In complete remission for >= 1 year, or

               -  Completely resected basal cell or squamous skin carcinoma, or

               -  In situ squamous cell carcinoma (SCC) of the cervix or anus

          -  Participants with grade >= 3 peripheral neuropathy

          -  Participants with a history of venous or arterial thromboembolism, unless line-rated
             thrombosis without embolus occurring >= 1 year prior to study entry

          -  Participants with a known procoagulant disorder including prothrombin gene mutation
             20210, antithrombin III deficiency, protein C deficiency, protein S deficiency, or
             antiphospholipid syndrome, but not including heterozygosity for the Factor V Leiden
             mutation or the presence of a lupus anticoagulant in the absence of other criteria for
             the antiphospholipid syndrome

          -  Participants with any prior use of pomalidomide, lenalidomide or thalidomide

          -  Participants with any condition, including the presence of laboratory abnormalities,
             which in the opinion of the responsible investigator places the participant at
             unacceptable risk if they were to participate in the study or confounds the ability to
             interpret data from the study