EphA2 siRNA in Treating Patients With Advanced or Recurrent Solid Tumors

Inclusion Criteria: * All patients with histologic proof of advanced solid tumors, who are not candidates for known regimens or protocol treatments of higher efficacy or priority * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * All patients (dose escalation and dose expansion phases) must be willing to undergo pre- and post-treatment biopsies * For the dose escalation phase, the trial population will be limited to solid tumor types * For dose expansion phase: patients must have EphA2 overexpression overall H-score of 3 or above in immunohistochemistry (IHC) evaluation; Clinical Laboratory Improvement Amendments (CLIA) certified EphA2 IHC staining to be performed on formalin fixed, paraffin-embedded tissue sections using monoclonal EphA2 antibody; EphA2 expression to be assessed through a combo of % of positive cells and staining intensity; the % of positive cells will be rated: 0 points (pts), 0 to 5%; 2 pts, 6 to 50%; 3 pts, 50%; the staining intensity will be rated as follows: 1 pt, weak intensity; 2 pts, moderate intensity; 3 pts, strong intensity; pts for expression and % of positive cells will be added; an overall score will be assigned; tumors to be categorized into 4 groups: negative (overall score 0), 5% cells stained, regardless of intensity; weak expression (overall score 1), 1 - 2 pts; moderate expression (overall score 2), 3 - 4 pts; and strong expression (overall score 3), 5 - 6 pts; overall H-score of 3 or above will be defined as EphA2 overexpression in tumor cells * Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension; at least one biopsiable lesion must be available; when imaging (DCE-MRI, DW-MRI and PET-computed tomography \[CT\] imaging) is being performed for secondary objectives (dose level III \[or when the dose reaches at least 1,500 ug/m\^2\] and during the expansion phase) at least one lesion (\>= 2 cm) not adjacent to the diaphragm will be required when measured by conventional techniques, including palpation, plain x-ray, CT, and MRI; a second lesion accessible for biopsy must also be present; patients must have at least one 'target lesion' to be used to assess response on this protocol as defined by Response Evaluation Criteria in Solid Tumors (RECIST); this may be one of the lesions mentioned above; tumors within a previously irradiated field will be designated as 'non-target' lesions * Resolution of any effects of prior therapy (except alopecia) to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.03 grade =\< 1 and to baseline laboratory values as defined below * Hemoglobin (HGB) \>= 9 g/dL * White blood cells (WBC) \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelet (PLT) \>= 100,000/mcL * Total bilirubin less than or equal to 1.5 * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) \< 2.5 x institutional upper limit of normal (ULN) * Creatinine \< 1.5 x ULN or creatinine clearance \> 60 ml/min according to Cockcroft-Gault formula * Neuropathy (sensory and motor) =\< to CTCAE grade 1 * Prothrombin time (PT) such that international normalized ratio (INR) is \< 1.5 (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin or low molecular weight heparin) and a partial thromboplastin time (PTT) \< 1.2 times control * Patients should be free of active infection requiring intravenous antibiotics * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration (study enrollment); continuation of hormone replacement therapy is permitted; stable regimens of hormonal therapy i.e. for prostate cancer (e.g. leuprolide, a gonadotropin-releasing hormone \[GnRH\] agonist), ovarian or breast cancer are not exclusionary * Any other prior therapy directed at the malignant tumor, including immunologic agents, must be discontinued at least three weeks prior to first dose of study drug (6 weeks for nitrosoureas or mitomycin C) * Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intrauterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study and for at least 3 months after completion of EphA2 siRNA-DOPC therapy * Male subject agrees to use an acceptable method of contraception for the duration of the study * Patients must voluntarily sign an informed consent indicating that they are aware of the investigational nature of this study in keeping with the policies of the hospital Exclusion Criteria: * Patients may not be receiving any other investigational agents and/or other therapy for their cancer * History of allergic reactions attributed to compounds of similar chemical or biologic composition to DOPC, Magnevist, or fluorodeoxyglucose (FDG) * Patients with active bleeding or pathologic conditions that carry high risk of bleeding, such as a known bleeding disorder, coagulopathy, or tumor involving major vessels * Patients with history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases * Patients with history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within 6 months of the first date of treatment on this study * Patients with clinically significant cardiovascular disease; this includes: uncontrolled hypertension (greater than 140/90); myocardial infarction or unstable angina within 6 months prior to registration; New York Heart Association (NYHA) grade II or greater congestive heart failure; serious cardiac arrhythmia requiring medication; grade II or greater peripheral vascular disease; patients with clinically significant peripheral artery disease, e.g., those with claudication, within 6 months of first date of treatment on this study * Patients whose circumstances do not permit completion of the study or the required follow-up * Patients who are pregnant or nursing * History of human immunodeficiency virus (HIV) or HIV-positive patients on combination antiretroviral therapy are ineligible * Patients whose tumor is not accessible for a core biopsy * Exclusion criteria (MRI specific): * Patients who are ineligible to undergo an MRI scan for reasons such as claustrophobia or the presence of implanted devices or metallic foreign bodies that are not magnetic resonance (MR) compatible; patients with a known history of allergic reaction to gadolinium contrast agents; patients with a history of a glomerular filtration rate (GFR) of less than 60 or acute renal disease * Exclusion criteria (PET specific): * Pregnant or nursing women; extreme claustrophobia; weight near or greater than 350 pounds