Pomalidomide in Treating Patients With Kaposi Sarcoma and Human Immunodeficiency Virus Infection

Inclusion Criteria: * Participants must have measurable cutaneous KS that has been pathologically confirmed by an acquired immunodeficiency syndrome (AIDS) Malignancy Consortium (AMC)-approved pathologist; diagnostic tissue must be available to satisfy the tissue submission requirements for central pathology review * Participants may not show evidence for ongoing improvement in KS lesions in the 4 weeks prior to enrollment * HIV positive. Documentation of HIV-1 infection by means of any one of the following: * HIV-1 RNA detection by a licensed HIV-1 RNA assay demonstrating \>1000 RNA copies/mL confirmed by a licensed screening antibody and/or HIV antibody antigen combination assay; * 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. 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 E/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 RNA viral load. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky performance status \[KPS\] \>= 50) * Life expectancy \>= 12 weeks * Hemoglobin \>= 8 g/dL * Absolute neutrophil count (ANC): \>= 1,000 cells/mm\^3 (1.0 x 10\^9/L) * Platelets: \>= 75,000 cells/mm\^3 (75.0 x 10\^9/L) * Total bilirubin: =\< 1.5 times the upper limit of normal (ULN), unless the participant is receiving an antiretroviral drug known to be associated with increased bilirubin, in which case the direct fraction should be =\< 2 times the ULN * Serum aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT) / alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x ULN * Estimated or measured creatinine clearance \> 60 mL/minute (1.00 mL/s) (serum creatinine =\< 2.0 mg/dL / 176.8 umol/L) * Currently receiving local standard of care antiretroviral therapy (ART) for \>= 12 weeks, with HIV viral load =\< 400 copies/mL; participants are required to be on antiretroviral regimens that are in accordance with the current International AIDS Society guidelines concurrently with chemotherapy; the specific agents are at the discretion of the investigator and the use of investigational agents currently available on an expanded access basis is allowed * A female of childbearing potential (FCBP) is a female who has achieved menarche at some point and who meets one of the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy, or 2) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months), or 3) does not have a serum or plasma follicle stimulating hormone (FSH) \> 40 mIU/mL and a history of amenorrhea x \>= 1 year * FCBP 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, including one of the following highly effective, long-acting methods, DepoProvera, an intrauterine device (IUD), an implant\*, or bilateral tubal ligation, if it can be verified that the procedure was performed, 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 * NOTE: Implants containing levonorgestrel and etonogestrel are prohibited in women receiving efavirenz, as drug interactions will render the implants ineffective * Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a vasectomy * All participants must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure; serum or urine pregnancy testing will be repeated in FCBP, and must be negative, within 24 hours of starting each new cycle of pomalidomide * Able to take aspirin (\>= 81 mg) daily as prophylactic anticoagulation * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants who are receiving any other investigational agents * Any prior use of thalidomide, lenalidomide, or pomalidomide * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pomalidomide * Visceral disease requiring cytotoxic chemotherapy (i.e., pulmonary KS, symptomatic gastrointestinal KS). KS-related lymphedema is permitted. * Use of agents containing zidovudine (including Combivir and Trizivir) are prohibited; in order to be eligible, participants taking zidovudine must change to a different regimen at least 7 days prior to therapy initiation; changes to antiretroviral therapy (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 * Use of erythropoietin is prohibited * Co-administration of corticosteroids greater than doses required for treatment of adrenal insufficiency is prohibited * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection for which the participant has not completed at least 14 days of therapy prior to study enrollment and/or is not clinically stable; 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; breastfeeding should be discontinued if the mother is treated with pomalidomide * Specific KS therapy, including cytotoxic chemotherapy but not including ART, within the past 4 weeks * Use of other anticancer treatments or agents within the past 4 weeks * History of malignant tumors other than KS, unless: * In complete remission for \>= 1 year, or * Completely resected basal cell carcinoma, or * In situ squamous cell carcinoma of the cervix or anus * Grade \>= 1 peripheral neuropathy * History of myocardial infarction (MI), cerebrovascular accident, or venous or arterial thromboembolism, unless line-related thrombosis without embolus occurring within 1 year prior to study entry * Known procoagulant disorder including prothrombin gene mutation 20210, antithrombin III deficiency, protein C deficiency, protein S deficiency and 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 * Any condition, including the presence of current laboratory abnormalities or other factor that, in the opinion of the 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