Apixaban in Preventing Secondary Cancer Related Venous Thrombosis in Cancer Patients Who Have Completed Anticoagulation Therapy

Inclusion Criteria: * Confirmed acute index (original venous thrombotic) event: lower extremity or upper extremity (jugular, innominate, subclavian, axillary, brachial) DVT, PE, splanchnic (hepatic, portal, splenic, mesenteric, renal, gonadal), or cerebral vein thrombosis for which the patient has received \>= 180 days (but =\< 365 days) of anticoagulant therapy prior to registration; the date, imaging modality, and location of index event will be required; the date of initiation and specific type of anticoagulants used will also be required * Active cancer defined as metastatic disease and/or any evidence of cancer on cross-sectional or positron emission tomography (PET) imaging, cancer related surgery, chemotherapy or radiation therapy within the past 6 months; Note: non-melanoma skin cancer does not meet the cancer requirement * Life expectancy \>= 6 months * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0, 1, or 2 * Hemoglobin \>= 8 g/dL obtained =\< 30 days prior to registration * Platelet count \>= 50,000/mm\^3 obtained =\< 30 days prior to registration * Alanine aminotransferase (ALT) or aspartate transaminase (AST) =\< 3 x upper limit of normal (ULN) obtained =\< 30 days prior to registration * Calculated creatinine clearance must be \>= 30 ml/min using the Cockcroft-Gault formula obtained =\< 30 days prior to registration * Negative serum or urine pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only; * Note: a woman of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) and is not postmenopausal; menopause is defined as 12 months of amenorrhea in a woman over age 45 years in the absence of other biological or physiological causes * Ability to provide informed written consent * Willing to undergo monthly follow-up assessment, either in person at the enrolling institution or by telephone Exclusion Criteria: * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Note: women of child bearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug (s) plus 33 days after finishing the last dose * Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug (s) plus 93 days after finishing the last dose * Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements; however they must still undergo pregnancy testing as described in this section; note: investigators shall counsel WOCBP and male subjects who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy; investigators shall advise WOCBP and male subjects who are sexually active with WOCBP on the use of highly effective methods of contraception; highly effective methods of contraception have a failure rate of \< 1% when used consistently and correctly; at a minimum, subjects must agree to the use of one method of highly effective contraception as listed below: * Male condoms with spermicide * Hormonal methods of contraception including combined oral contraceptive pills, vaginal ring, injectables, implants and intrauterine devices (IUDs) such as Mirena by WOCBP subject or male subject's WOCBP partner * Female partners of male subjects participating in the study may use hormone based contraceptives as one of the acceptable methods of contraception * IUDs, such as ParaGard * Tubal ligation * Vasectomy * Complete abstinence * Complete abstinence is defined as complete avoidance of heterosexual intercourse and is an acceptable form of contraception for all study drugs; acceptable alternate methods of highly effective contraception must be discussed in the event that the subject chooses to forego complete abstinence * Active major bleeding * Severe hypersensitivity reaction to apixaban (e.g., anaphylactic reactions) * Current use of strong CYP3A4 inducers or inhibitors * NOTE: patients may be eligible if they transition to an alternative agent or are able to stop CYP3A4 inducer or inhibitor * Current use of thienopyridine therapy (clopidogrel, prasugrel, or ticagrelor) that will be continued on study * Severe liver disease (known cirrhosis Childs Pugh class B or C), or active hepatitis * Documented venous thromboembolism while on therapeutic anticoagulation ("anticoagulation failure") * Mechanical heart valve * Documented hemorrhagic tendencies (e.g., hemophilia) * Bacterial endocarditis * Any of the following conditions: * Intracranial bleeding =\< 6 months prior to randomization * Intraocular bleeding =\< 6 months prior to randomization * Gastrointestinal bleeding and/or endoscopically proven ulcer =\< 6 months prior to randomization * Head trauma or major trauma =\< 1 month prior to randomization * Neurosurgery =\< 2 weeks prior to randomization * Major surgery =\< 1 week prior to randomization * Gross hematuria at the time of randomization