Ramucirumab in Treating Patients With Advanced or Metastatic, Previously Treated Biliary Cancers That Cannot Be Removed by Surgery

Inclusion Criteria: * Patient must have cholangiocarcinoma, gallbladder cancer or adenocarcinoma on liver biopsy with clinical features consistent with biliary primary/cholangiocarcinoma * Metastatic or unresectable disease documented on diagnostic imaging studies * Must have received at least one regimen containing gemcitabine chemotherapy * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Total bilirubin =\< 1.5 mg/dL (25.65 mol/L) * Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3.0 times the upper limit of normal (\[ULN\]; or 5.0 times the ULN in the setting of liver metastases) * Absolute neutrophil count (ANC) \>= 1000/uL * Hemoglobin \>= 9 g/dL (5.58 mmol/L) * Platelets \>= 100,000/uL * The patient does not have: * Cirrhosis at a level of Child-Pugh B (or worse) or * Cirrhosis (any degree) and a history of hepatic encephalopathy or clinically meaningful ascites resulting from cirrhosis; clinically meaningful ascites is defined as ascites from cirrhosis requiring diuretics or paracentesis * Serum creatinine =\< 1.5 times the ULN or * Creatinine clearance (measured via 24-hour urine collection) \>= 40 mL/minute (that is, if serum creatinine is \> 1.5 times the ULN, a 24-hour urine collection to calculate creatinine clearance must be performed * The patient's urinary protein is =\< 1 positive (+) (=\< 30-100 mg/dl) on dipstick or routine urinalysis (urinary analysis \[UA\]; if urine dipstick or routine analysis is \>= 2+ (\>=100-300 mg/dl), a 24-hour urine collection for protein must demonstrate \< 1000 mg of protein in 24 hours to allow participation in this protocol) * The patient must have adequate coagulation function as defined by international normalized ratio (INR) =\< 1.5 and * Partial thromboplastin time (PTT) (PTT/activated partial thromboplastin time \[aPTT\]) \< 1.5 x ULN) * Patients on full-dose anticoagulation must be on a stable dose (minimum duration 14 days) of oral anticoagulant or low molecular weight heparin; if receiving warfarin, the patient must have an INR =\< 3.0 and no active bleeding (that is, no bleeding within 14 days prior to first dose of protocol therapy) or pathological condition present that carries a high risk of bleeding (for example, tumor involving major vessels or known varices) * The patient, if sexually active, must be postmenopausal, surgically sterile, or using effective contraception (hormonal or barrier methods) * Female patients of childbearing potential must have a negative serum pregnancy test within 7 days * Patients must sign an informed consent and authorization indicating that they are aware of the investigational nature of this study and the known risks involved * In the ten patient expanded cohort, patients diagnosed with deoxyribonucleic acid (DNA) repair or FGFR genetic aberrations will be enrolled Exclusion Criteria: * The patient has experienced any grade 3-4 gastrointestinal (GI) bleeding within 3 months prior to enrollment * Prior therapy with any agent targeting the vascular endothelial growth factor receptor (VEGFR) pathway to include bevacizumab, pazopanib, and other anti-angiogenesis inhibitors * The patient has a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism, including portal venous thrombosis (venous port or catheter thrombosis, incidental pulmonary embolism diagnosed on imaging studies or superficial venous thrombosis are not considered significant) during the 3 months prior to randomization * The patient has experienced any arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to enrollment * The patient has uncontrolled or poorly-controlled hypertension (\> 160 mmHg systolic or \> 100 mmHg diastolic for \> 4 weeks) despite standard medical management * The patient has a serious or non-healing wound, ulcer, or bone fracture within 28 days prior to enrollment * The patient has undergone major surgery within 28 days prior to enrollment, or subcutaneous venous access device placement within 7 days prior to enrollment * The patient is receiving chronic antiplatelet therapy, including aspirin, nonsteroidal anti-inflammatory drugs (\[NSAIDs\], including ibuprofen, naproxen, and others), dipyridamole or clopidogrel, or similar agents; once-daily aspirin use (maximum dose 325 mg/day) is permitted * The patient has elective or planned major surgery to be performed during the course of the clinical trial * The patient is pregnant or breast-feeding