sEphB4-HSA in Treating Participants With BCG-Unresponsive or Refractory Bladder Cancer

Inclusion Criteria: * Patients with bladder CIS, or completely resected high grade Ta/T1 lesions that are BCG unresponsive; unresponsive is BCG refractory and/or BCG relapsing * BCG refractory: persistent high-grade disease at 6 months despite receiving at least 5-6 induction instillations and at least one maintenance (two of three instillations) in a 6 month period * BCG relapsing: recurrence of high-grade disease after achieving a disease-free state at 6 months after receiving at least 5-6 induction instillations and at least one maintenance (two of three instillations) in a 6 month period * Eastern Cooperative Oncology Group performance status 0 to 2 * Written informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal health information * NOTE: HIPAA authorization may be included in the informed consent or obtained separately * Females must not be breastfeeding * Patients must be willing to undergo additional radiologic imaging while on study * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcl * Total bilirubin =\< 1.5 X institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine =\< 1.5 X institutional upper limit of normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days following completion of therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) * Ability to understand and the willingness to sign a written informed consent * Absence of concomitant upper tract urothelial carcinoma (i.e. cancer within the kidney or ureter) as evidenced on computed tomography (CT) urogram and no visible lesion and/or biopsy proven evidence of urothelial carcinoma within the prostatic urethra (i.e. biopsy proven presence of cancer within the prostatic urethra) * Patient has a desire to preserve organ, understanding the risks of delaying standard of care * Patient is ineligible, declines, or is considered ineligible to undergo radical cystectomy Exclusion Criteria: * If they are undergoing or have undergone in the past 4 weeks (28 days) any other therapy for their cancer, including radiation therapy and chemotherapy * If they have a major systemic infection requiring antibiotics 72 hours or less prior to the first dose of study drug * If they have untreated central nervous system (CNS) metastasis; patients whose CNS metastases have been treated by surgery or radiotherapy, who are no longer on corticosteroids, and who are neurologically stable may be enrolled in the dose escalation portion of the trial * If they have New York Heart Association (NYHA) class 3 or 4; myocardial infarction, acute coronary syndrome, 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 patient at undue risk for treatment related complications * If they have any other condition, including mental illness or substance abuse, deemed by the investigator to be likely to interfere with a patient?s ability to sign informed consent, cooperate and participate in the study, or interferes with the interpretation of the results * If they are pregnant or lactating * If they are on any dose of warfarin or are on full dose anticoagulation with other agents, including low molecular weight heparin, antithrombin agents, anti-platelet agents and full dose aspirin within 7 days prior to first dose of study drug; patients on prophylactic doses of low-molecular weight heparin are allowed * If they have had any active bleeding in the last =\< 4 weeks or have an otherwise known bleeding diathesis * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to agent(s) or other agents used in study * 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 * Patients must not be pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants * Evidence of a history of a stroke or myocardial infarction within the last 6 months prior to study enrollment * Previous intravesical immunotherapy less than 3 months before study entry; Note: if a patient is eligible for the study but has had intravesical immunotherapy within the past 3 months, they can enroll in the study and initiation of treatment of the drug will be delayed until a minimum of 90 days has passed since the previous treatment * Renal and hepatic function values exceeding 2 times the upper normal value * Patients who cannot hold instillation for 2 hours * Patients who cannot tolerate intravesical dosing or intravesical surgical manipulation