Recombinant Albumin Fusion Protein sEphB4-HSA in Treating Patients With Metastatic or Recurrent Solid Tumors

Inclusion Criteria:

* For expansion Cohort A: Advanced (metastatic or recurrent) pathologically proven solid tumor which has not responded to standard therapy or which has progressed following standard therapy for advanced disease and/or for which no standard therapy is known to be effective. Measurable disease required.
* For expansion Cohort B: Advanced pathologically proven mutant KRAS non-small cell lung cancer (group 1), pancreatic cancer (group 2; documentation of KRAS mutation not required), mutant KRAS colorectal cancer (group 3), head and neck squamous cell carcinoma (group 4) mesothelioma (group 5), hepatocellular cancer (group 6), and biliary carcinoma (group 7). Measurable disease required.
* Must agree, as part of the informed consent, to provide blood and tumor samples for molecular correlates, pharmacokinetics and pharmacodynamics. Patients in expansion cohort A must have tumor sites that are accessible for tumor biopsy and must agree to undergo a pre-treatment and post-treatment biopsy. Patients in cohort B group 3 \& 4 must have tumor sites that are accessible for tumor biopsy and must agree to undergo a pre-treatment and post-treatment biopsy.
* Must have an Eastern Cooperative Oncology Group (ECOG) performance score of 0-1
* Life expectancy of at least 12 weeks
* Patients or their legal representatives must be able to comprehend and provide written informed consent
* White blood count (WBC) \>= 3,000/μl
* Absolute neutrophil count (ANC) \>= 1,500/μl
* Platelet count \>= 100,000/μl (except in hepatocellular carcinoma patients with portal hypertension for whom a platelet count of \>= 70,000/μl is allowed)
* Serum creatinine =\< 1.5 X upper limit of normal (ULN) for reference lab
* Creatinine Clearance of \>= 60 (as calculated by Cockcroft-Gault formula
* Serum bilirubin =\< 1.5 mg/dL
* Serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels =\< 3X the ULN for the reference lab (=\< 5X the ULN if there is evidence of hepatic involvement by malignant disease)
* Recovered to grade 1 from the effects (excluding alopecia) of any prior therapy for their malignancies
* Women of childbearing potential (WOCBP) and male patients with WOCBP partner must be using an adequate method of contraception to avoid pregnancy throughout the study and for up to 12 weeks after the last dose of investigational product in such a manner that the risk of pregnancy is minimized
* WOCBP must have a negative serum test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 72 hours prior to the start of study drug
* Patients with hepatitis B infection must be on appropriate antiviral therapy
* For cohort B, group 1: Non-small cell lung cancer:

  * Must have advanced non-small cell lung cancer with mutant KRAS
  * Must have failed a minimum of one previous line of chemotherapy for advanced disease
* For cohort B, group 2: Pancreatic cancer:

  * Must have failed a minimum of one previous line of therapy for advanced disease
* For cohort B, group 3: Colorectal cancer:

  * Must have colorectal adenocarcinoma that harbor a KRAS mutation
  * Must have failed a minimum of one previous line of chemotherapy
* For cohort B, group 4: Head and neck squamous cell cancer:

  * Must have failed a platinum based chemotherapy regimen that was administered for advanced disease with a palliative intent; patients treated with concurrent platinum agent and radiation as definitive therapy are not eligible unless they subsequently received another line of systemic therapy.
* For cohort B, group 5: Mesothelioma:

  * Must have histologically or cytologically proven diagnosis of malignant mesothelioma; both pleural and peritoneal mesothelioma are allowed
  * Must have failed a minimum of one previous line of systemic therapy for advanced disease
* For cohort B, group 6: Hepatocellular carcinoma:

  * Patients with hepatocellular carcinoma do not need to have histologic confirmation of disease as long as they meet the radiologic criteria for diagnosis of HCC (evidence of arterial phase enhancement with corresponding venous or delayed phase wash out).
  * Must have advanced disease that is not amenable for resection or transplantation, and that is not treatable with liver directed modalities such as radiofrequency ablation or transarterial chemoembolization
  * Patients are not required to have failed Sorafenib
* For cohort B, group 7: Gallbladder cancer or cholangiocarcinoma:

  * Must have failed a minimum of one previous line of systemic therapy for advanced disease. If patient has had decompression of the biliary tree within the last 14 days, stability of the bilirubin level needs to be confirmed with two measurements that are within 5 to 7 days of each other.

Exclusion Criteria:

* Undergoing or have undergone in the past 28 days any other therapy for their cancer, including radiation and adjuvant therapy
* Major systemic infection requiring antibiotics 72 hours or less prior to first dose of study drug
* Untreated central nervous system (CNS) metastases; 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
* 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 sEphB4HSA or places the patient at undue risk for treatment related complications
* 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
* Pregnant or lactating
* 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 first dose of study drug; patients on prophylactic doses of low-molecular weight heparin are allowed
* Any active bleeding in the last =\< 4 weeks or have an otherwise known bleeding diathesis
* QTcF (Fridericia Correction Formula) \> 480 on 2 out of 3 EKG's (if first EKG is \< 480, no need to repeat, if first EKG is \> 480 repeat twice for a total of 3 EKG's)
* For cohort B, group 1: Non-small cell lung cancer:

  * Must not have clinically significant active hemoptysis
* For cohort B, group 4: Head and neck squamous cell cancer:

  * Must not have evidence of major vessel involvement or encasement by tumor
* For cohort B, group 6: Hepatocellular Carcinoma:

  * Child Pugh score \> 7
  * Ascites that is not medically controlled or that required a therapeutic paracentesis within last 3 months
  * Any episode of hepatic encephalopathy within the previous 6 months
  * Variceal bleeding within last 6 months
  * Patients with evidence of portal hypertension must have had an EGD within last year with appropriate treatment of esophageal varices as per standard of care