Ziv-Aflibercept Followed by Ziv-Aflibercept, Fluorouracil, and Leucovorin Calcium in Treating Patients With Stage IV Colorectal Cancer

Inclusion Criteria: * Histologically confirmed stage IV colorectal adenocarcinoma previously treated with FOLFOX and FOLFIRI and bevacizumab, receipt of cetuximab or panitumumab is not required, and has shown progression or intolerant of both oxaliplatin and irinotecan-based regimens; baseline tumor assessments must be done within 28 days of starting treatment * Patients must have lesions that can be easily biopsied * Representative tumor tissue specimens (paraffin block preferred) * Signed informed consent prior to initiation of any study-specific procedure or treatment, including agreement to two biopsies during the study * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Able to comply with the protocol, including tissue and blood sampling * Leukocytes \>= 3,000 per mm\^3 * Absolute neutrophil count \>= 1,000 per mm\^3 * Platelet count \>= 75,000 per mm\^3 * Hemoglobin \>= 9 g/dL (may be transfused to maintain or exceed this level) * Creatinine clearance according to the Cockcroft and Gault formula of \>= 50 mL/min * Urine for proteinuria should be \< 2 +; patients discovered to have \>= 2 + proteinuria on dipstick urinalysis at baseline should undergo a 24-hour urine collection and must demonstrate \< 1 g of protein in 24 hours * Total bilirubin \< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase and alanine aminotransferase \< 2.5 x ULN * International normalized ratio =\< 1.5 and activated prothrombin time =\< 1.5 x ULN for patients not receiving anti-coagulation therapy * The use of full-dose oral or parenteral anticoagulants is permitted as long as the international normalized ratio (INR) or activated partial thromboplastin time (aPTT) is within therapeutic limits (according to the medical standard of the enrolling institution), and the patient has been on a stable dose of anticoagulants for at least two weeks prior to the first study treatment * Female patients should not be pregnant or breast-feeding * A 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 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 months) * Female patients with childbearing potential should agree to use effective, non-hormonal means of contraception (intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal jelly or surgically sterile) during the study and for a period of at least 6 months following the last administration of study drug * Female patients with an intact uterus (unless amenorrheic for the last 24 months) must have a negative serum pregnancy test within 7 days prior to randomization into the study * Male patients must agree to use effective contraception during the study and for a period of at least 6 months following the last administration of study drugs, even if they have been surgically sterilized Exclusion Criteria: * Any prior systemic treatment with targeted antiangiogenic agents except for bevacizumab; receipt of cetuximab or panitumumab is not an exclusion criteria * Radiotherapy to any site for any reason within 14 days prior to treatment * Uncontrolled intercurrent illness including, but not limited to * Any of the following within 6 months prior to inclusion: myocardial infarction, severe/unstable angina pectoris, coronary/peripheral artery bypass graft, New York Heart Association (NYHA) class III or IV congestive heart failure, stroke or transient ischemic attack * Any of the following within 3 months prior to inclusion: grade 3-4 gastrointestinal bleeding/hemorrhage (unless due to resected tumor), treatment resistant peptic ulcer disease, erosive esophagitis or gastritis, infectious or inflammatory bowel disease, diverticulitis, pulmonary embolism or other uncontrolled thromboembolic event * History of allergic reactions attributed to compounds of similar chemical or biologic composition to agents used in the study * History of arterial thromboembolic events * History of abdominal fistula formation, gastrointestinal perforation, or abdominal abscess within six months * History or evidence of inherited bleeding diathesis or coagulopathy with a risk of bleeding * Patients must not be pregnant or nursing * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days before start of study drug * Any hemorrhage or bleeding event \>= CTCAE grade 3 within 4 weeks prior to the start of study medication * Non-healing wound, ulcer, or bone fracture * Inadequately controlled hypertension (systolic blood pressure \[SBP\] \> 150 mmHg, diastolic blood pressure \[DBP\] \> 100 mg Hg) * Known positivity for human immunodeficiency virus (HIV) * Malignancies other than colorectal adenocarcinoma within 5 years prior to treatment, except for adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, and ductal carcinoma in situ treated surgically with curative intent * Clinically detectable (by physical exam) third-space fluid collections (e.g. ascites or pleural effusion) that cannot be controlled by drainage or other procedures prior to study entry * Treatment with any other investigational agent, or participation in another investigational drug trial within 28 days prior to randomization * Patients can withdraw consent anytime during the study