Pomalidomide Treatment in Patients With Kaposi Sarcoma

Inclusion Criteria: * Participant is able to understand and willing to sign a written informed consent document * Participants must have histologically or cytologically confirmed cutaneous KS. 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 into OPEN Step-1 (Treatment Assignment - Registration Step). * 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 multi-spot 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 * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of pomalidomide in participants \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Life expectancy of greater than 6 months * Hemoglobin \>= 8 g/dL (within 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * Absolute neutrophil count (ANC): \>= 1,000/mm\^3 (within 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * Platelets: \>= 75,000/mm\^3 (within 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * 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 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN (within 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * 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 14 days before enrollment into OPEN Step-1 (Treatment Assignment - Registration Step) * 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 post menopausal 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 (± 2) 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 into OPEN Step-1 (Treatment Assignment - Registration Step). 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 one of the alternatives * 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 cytochrome P450 (CYP)1A2, 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 into OPEN Step-1 (Treatment Assignment - Registration Step) 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 analog 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 into OPEN Step-1 (Treatment Assignment - Registration Step) * Participants with high clinical suspicion of concurrent Castleman disease or IL6 related inflammatory disease * For a reference of signs and symptoms consistent with IL6 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 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