Nelfinavir Mesylate in Treating Patients With Kaposi Sarcoma

Inclusion Criteria: * Biopsy-proven KS involving skin (with or without visceral involvement) without need for urgent cytotoxic therapy; there should be no evidence of improvement in KS in the 4 weeks immediately prior to study enrollment * Known human immunodeficiency virus (HIV)-1 infection status, as documented by any nationally approved, licensed HIV rapid test performed in conjunction with screening (or enzyme-linked immunosorbent assay \[ELISA\], test kit, and confirmed by approved test at each study site; United States (U.S.) participants only: alternatively, this documentation may include a record demonstrating that another physician has documented the participant's HIV status based on either: * Approved diagnostic tests, or * The referring physician's written record that HIV infection was documented, with supporting information on the participant's relevant medical history and/or current management of HIV infection * Participants enrolled outside the U.S. must have a confirmatory diagnostic test sequence as appropriate per national standards, detailed as above, performed regardless of prior documented HIV status; for HIV-negative participants, testing must be performed no more than 1 month prior to study enrollment; NOTE: the term "licensed" refers to a U.S. Food and Drug Administration (FDA)-approved kit or for sites located in countries other than the United States, a kit that has been certified or licensed by an oversight body within that 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 enzyme/chemiluminescence immunoassay (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 ribonucleic acid (RNA) viral load * Participant may be either previously untreated for KS or refractory to or intolerant of any one or more prior KS therapies * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%) * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Total bilirubin: within normal limits at each study site local laboratory * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine transaminase (ALT) (serum glutamate-pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine levels =\< upper limit of institutional normal; or creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal * HIV seropositive participants must be on antiretroviral therapy (ART) with the following criteria: * A complete ART regimen that does not include the study drug as one of a minimum of 3 active drugs, which may include an integrase inhibitor or efavirenz in combination with nucleoside reverse-transcriptase inhibitors (NRTIs) * The ART regimen must not include protease inhibitor (PIs); participants must not have received a PI-based regimen for at least 4 weeks prior to enrollment * Participants must either have an undetectable HIV plasma ribonucleic acid (RNA), or if plasma RNA detectable, must be on the same stable regimen for a minimum of 12 weeks prior to study enrollment * No minimum cluster of differentiation (CD)4 count, but maximum HIV plasma RNA of 1,000 copies/mL * Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study enrollment and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she 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 Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to study enrollment or those who have not recovered from adverse events due to agents administered more than 4 weeks prior to study enrollment * Participants who are receiving any other investigational agents * Participants with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nelfinavir * Participants receiving any medications or substances that have antiviral activity against KSHV or that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A (CYP3A) or cytochrome P450, family 2, subfamily C, polypeptide 19 (2C19) are ineligible; each ART regimen must be reviewed by the PI before determining eligibility to receive nelfinavir mesylate (NFV); sensitive substrates should be avoided; of the antiretroviral drugs, only delavirdine, nevirapine, cobicistat-boosted antiretrovirals (strong CYP3A4 inhibitor), maraviroc (sensitive CYP3A4 substrate), and PIs (strong CYP3A4 inhibitor) are excluded; the following drugs are also prohibited: Strong Inhibitors of CYP3A4: * Antibiotics: clarithromycin, erythromycin, telithromycin, troleandomycin * HIV: non-nucleoside reverse transcriptase inhibitors (delavirdine, nevirapine), protease inhibitors (ritonavir, indinavir, lopinavir/ritonavir, saquinavir), cobicistat-boosted antiretrovirals (e.g., elvitegravir); NOTE: Clinical trials have demonstrated that there are no clinically significant drug-drug interactions between nelfinavir and the following antiretrovirals: efavirenz (strong CYP3A4 inhibitor), etravirine (strong CYP3A4 inhibitor); therefore, these antiretrovirals will not be excluded * Antifungals: itraconazole, ketoconazole, voriconazole, fluconazole, posaconazole * Antidepressants: nefazodone * Antidiuretic: conivaptan * GI: cimetidine, aprepitant * Hepatitis C: boceprevir, telaprevir * Miscellaneous: seville oranges, grapefruit, or grapefruit juice and/or pomelos, star fruit, exotic citrus fruits, or grapefruit hybrids Strong Inducers of CYP3A4: * Glucocorticoids: cortisone (\> 50 mg), hydrocortisone (\> 40 mg), prednisone (\> 10 mg), methylprednisolone (\> 8 mg), dexamethasone (\> 1.5 mg) * Anticonvulsants: phenytoin, carbamazepine, primidone, phenobarbital and other enzyme inducing anti-convulsant drugs (EIACD) * Antibiotics: rifampin (rifampicin), rifabutin, rifapentine * Miscellaneous: St. John's Wort, modafinil Strong Inhibitors of CYP2C9: * Antifungals: fluconazole; lists including medications and substances known or with the potential to interact with the CYP3A or 2C19 Drugs with KSHV antiviral activity: * Participants receiving any medications or substances that may interfere with KSHV replication are ineligible Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list; medical reference texts such as the physicians' desk reference may also provide this information; as part of the enrollment/informed consent 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; lists include medications and substances known or with the potential to interfere with KSHV replication * 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 * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with high dose nelfinavir * Chronic diarrhea as defined by loose or watery stools occurring more than 3 times daily at baseline lasting more than 4 weeks or not abating on condition-appropriate therapy prior to study enrollment * Participant is \< 2 years free of another primary malignancy; exceptions include basal cell skin cancer, stage 0-I squamous cell cancer of the skin, cervical carcinoma in situ, anal carcinoma in situ * Use of systemic corticosteroid therapy (except for replacement doses of glucocorticoid and/or mineralocorticoid for adrenal insufficiency); inhaled or intranasal corticosteroids for allergic or bronchospastic conditions are permitted