sEphB4-HSA in Treating Patients With Kaposi Sarcoma

Inclusion Criteria: * Participants may be treatment naïve, refractory to or intolerant of one or more prior therapies, or treated with prior systemic treatment including but not limited to liposomal doxorubicin * Participants must have biopsy-proven KS involving skin with or without visceral involvement * If HIV-positive, any cluster of differentiation (CD)4 count will be allowed on study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofsky performance score (KPS) \>= 60% * Life expectancy of greater than 3 months * Absolute neutrophil count \>= 1,500/mcL\* * Participants may be receiving growth factor support to meet these criteria * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN * Creatinine within normal institutional limit for the reference lab OR creatinine clearance \>= 60 mL/min/1.73 m\^2 as calculated by Cockcroft-Gault formula for participants with creatinine levels above institutional normal * Participants must have cutaneous lesion(s) amenable to four (4) 5-mm tumor biopsies during the study (either 4 separate lesions measuring \>= 5 mm each OR 2 separate lesions measuring \>= 10 mm each) and at least five additional lesions measurable for assessment with no improvement over the past month * Females of childbearing potential (FCBP)\* must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 14 days prior to enrollment and again within 24 hours prior to starting cycle 1 of sEphB4-HSA; further, they 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 during receipt of sEphB4-HSA, and 12 weeks after discontinuation of sEphB4-HSA; 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 successful vasectomy * A female of childbearing potential is 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) * Documentation of HIV status; if participant is HIV positive, HIV-1 infection, as documented by any federally approved, licensed HIV rapid test performed in conjunction with screening (or enzyme-linked immunosorbent assay \[ELISA\], test kit, and confirmed by Western blot or other approved test); alternatively, this documentation may include a record demonstrating that another physician has documented the participant's HIV status based on either: 1) approved diagnostic tests, or 2) 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 * If the participant is HIV negative, documentation of a negative result for any federally approved, licensed HIV rapid test within 4 weeks prior to study enrollment will suffice; if the initial rapid test is positive, further approved confirmatory test results must be present to document the subject's HIV status * If participant is HIV positive, participants must be on a stable antiretroviral regimen for at least 12 weeks prior to study enrollment * There should be no evidence for improvement in KS in the 3 months prior to study enrollment, unless there is evidence for progression of KS in the 4 weeks immediately prior to study enrollment * Participants must, in the opinion of the investigator, be capable of complying with the protocol Exclusion Criteria: * Inability to understand and inability to provide informed consent * Participants who are receiving any other investigational agents * Participants who have had anti-neoplastic treatment for KS (including chemotherapy, radiotherapy, local treatment including topical fluorouracil \[5-FU\], biological therapy or investigational therapy) within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study OR those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * 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 sEphB4-HSA or other agents used in study * Participants who refuse antiretroviral therapy for HIV, if HIV positive * Concurrent, acute, active infection, or treatment for infection, other than oral thrush or genital herpes, within 14 days of enrollment * Participants for whom front-line cytotoxic therapy is indicated (i.e. symptomatic visceral or pulmonary KS or symptomatic KS impairing functional status) * Concurrent neoplasia requiring cytotoxic therapy * Participant is =\< 2 years free of another primary malignancy; exceptions include the following: * Basal cell skin cancer * Cervical carcinoma in situ * Anal carcinoma in situ * Any steroid treatment except for that required for replacement therapy in adrenal insufficiency, topical or injected testosterone for hypogonadism, or inhaled steroids for the treatment of asthma * Previous local therapy of any KS-indicator lesion unless the lesion has clearly progressed since that local treatment; any prior local treatment to indicator lesions regardless of the elapsed time should not be allowed unless there is evidence of clear-cut progression of said lesion * Female participants who are pregnant, lactating, or breast-feeding * Breastfeeding should be discontinued if the mother is treated with sEphB4-HSA * Participants with a recent history (\< 6 months) of a major infarct including but not inclusive to bowel ischemia, cerebral vascular accident, transient ischemic attack, myocardial infarction, limb ischemia, or skin necrosis * Participants with a QTcF (Fridericia correction formula) \> 480 ms on 2 out of 3 electrocardiograms (EKGs) (if first EKG is \< 480, no need to repeat, if first EKG is \> 480 repeat twice for a total of 3 EKGs) * Participants with uncontrolled sustained hypertension which will be defined as systolic blood pressure \> 140, and diastolic blood pressure \> 90, even with use of anti-hypertensive medications * Participants with a recent history (\< 6 months) of a major bleed which will be defined as a symptomatic bleeding in a critical area or organ, such as intracranial, intraspinal, intraocular, retroperitoneal, intraarticular or pericardial, or intramuscular with compartment syndrome, and/or bleeding causing a fall in hemoglobin level 2 grams/dL or more, or leading to transfusion of two or more units of whole blood or packed red cells * Participants on any dose of warfarin or are on full dose anticoagulation with other agents including low molecular weight heparin, antithrombin agents, antiplatelet agents and full dose aspirin within 7 days prior to study enrollment; participants on prophylactic doses of low molecular weight heparin and low dose anticoagulants are allowed. * Cardiac related illnesses including, but not limited to: * Symptomatic congestive heart failure including participants with grade III/IV cardiac disease as defined by the New York Heart Association functional criteria * Unstable angina pectoris * Cardiac arrhythmia * Proteinuria as defined as \> 2+ on urine dipstick; if dipstick urinalysis shows \>= 2+ proteinuria, 24-hour urine for protein must be \< 2 grams * Participants with diabetes mellitus with ketoacidosis or chronic obstructive pulmonary disease (COPD) requiring hospitalization in the preceding 6 months, or any other intercurrent medical condition that contraindicates treatment with sEphB4-HSA or places the participant at undue risk for treatment related complications * Physical or psychiatric illness/social situations that in the estimation of the investigator would limit compliance with study requirements or place the participant at high risk of toxicity or non-compliance