Brigatinib and Bevacizumab for the Treatment of ALK-Rearranged Locally Advanced, Metastatic, or Recurrent NSCLC

Inclusion Criteria: * Patients must have a histologically documented (either primary or metastatic site) diagnosis of locally advanced, recurrent, or metastatic ALK rearranged non-small cell lung cancer (NSCLC) * Patients must have shown progression on ALK-directed therapy * Note: Patients may have received more than one prior line of therapy, however, at least one of these must be an ALK-directed line of therapy * Patients must have measurable disease as per appropriate guidelines by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 * Patients must have the ability to understand and the willingness to sign a written consent prior to registration in the study * Patients with asymptomatic (as determined by the treating investigator) CNS metastasis are eligible for participation * Note: Patients with leptomeningeal disease are not eligible * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Patient life expectancy of more than 12 weeks * Patients must have adequate organ and bone marrow function during screening, as defined below: * Absolute neutrophil count \>= 1.5 x 10\^9/L * Hemoglobin \>= 9 g/dL * Note: Transfusions are permitted (transfusions \>= 1 day to registration are allowed) * Platelets \>= 75 x 10\^(9)/L * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Note: Patients with Gilbert syndrome are exempt * Alanine amino transferase and aspartate aminotransferase =\< 2.5 x ULN * Note: =\< 5 x ULN is acceptable if liver metastases are present * Serum lipase =\< 1.5 x ULN * Creatine kinase (CPK) \< 5.0 x ULN * Estimated glomerular filtration rate (eGFR) using the modification of diet in renal disease (MDRD) equation \>= 30 mL/min/1.73 m\^2 * Patients must meet criteria for appropriate contraception, listed as follows * Female patients must meet at least one of the following criteria: * Are postmenopausal with last menstrual period at least 1 year before registration, OR * Are surgically sterile, OR * If they are of childbearing potential, * Agree to practice 1 highly effective method of non-hormonal contraception and one additional effective (barrier) method at the same time, from the time of signing the informed consent through 180 days after the last dose of study drug, or * Agree to practice true abstinence, when is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g. calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) * Agree not to donate eggs (ova) during the course of this study or 180 days after receiving their last dose of study drug. Agree not to breast-feed for the duration of treatment through 6 months post treatment * Note: Female patients who are pregnant, planning a pregnancy, or nursing are not eligible * Male patients, even if surgically sterilized (i.e. status post-vasectomy), must: * Agree to practice effective barrier contraception during the entire study treatment period and through 180 days after the last dose of study drug, or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g. calendar, ovulation, symptothermal, postovulation methods for the female partner\] and withdrawal are not acceptable methods of contraception. Female and male condoms should not be used together.) * Agree not to donate sperm during the course of this study or within 180 days after receiving their last dose of study drug Exclusion Criteria: * Patients who have had prior systemic anticancer or radiotherapy =\< 14 days prior to first dose of brigatinib are not eligible * Patients may not have received any other investigational agents =\< 14 days prior to first dose of brigatinib * Patients who have received antineoplastic monoclonal antibodies within 21 days of the first dose of brigatinib, and tyrosine kinase inhibitors (TKIs) within 7 days of the first dose of brigatinib are not eligible * Patients with prior severe infusion reaction to bevacizumab are not eligible * Patients with other coexisting malignancies or malignancies diagnosed within the previous 3 years that per the investigator are at high-risk of relapse within one year are not eligible * Note: Exceptions to this include non-melanoma skin cancer, cervical cancer in-situ, well-differentiated thyroid cancer or prostate cancer. Other cancers that per assessment of the principal investigator (PI) are not prognosis-limiting can be allowed after review by the PI. If there is no evidence of disease for at least 3 years, patients may be eligible * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible: * Uncontrolled pulmonary, renal, or hepatic dysfunction, * Ongoing or active infection requiring systemic treatment including hepatitis B and hepatitis C, * Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection, * Note: Patients who have isolated positive hepatitis B core antibody (i.e. in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load * Active uncontrolled infection or severe infectious disease such as severe pneumonia, meningitis, or septicemia, * Known active or chronic viral hepatitis or human immunodeficiency virus (HIV), * Psychiatric illness/social situations that would limit compliance with study requirements * Patients with any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints are not eligible * Female patients who are pregnant, planning a pregnancy, or nursing or have a positive serum pregnancy test within 7 days prior registration (without subsequent negative vaginal ultrasound) are not eligible * Patients who have had major surgery within 30 days of registration, are not eligible * Note: Minor surgical procedures such as catheter placement or minimally invasive biopsies are allowed * Patients who have significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to the following are not eligible: * Myocardial infarction within 6 months before registration * Unstable angina within 6 months before registration * Congestive heart failure within 6 months before registration * History of clinically significant atrial arrhythmia (including clinically significant bradyarrhythmia), as determined by the treating physician * Any history of clinically significant ventricular arrhythmia * Patients who have had a cerebrovascular accident or transient ischemic attack within 6 months before registration are not eligible * Patients who have uncontrolled hypertension are not eligible * Note: Patients with hypertension per the opinion of the treating investigator should be under treatment on study entry to control blood pressure * Patients who have the presence at baseline of unresolved pulmonary interstitial disease that is grade 3 or 4 are not eligible * Patients who have a history of or the presence at baseline of grade 2 or higher uncontrolled drug related pneumonitis, or radiation pneumonitis are not eligible * Patients who have malabsorption syndrome or other gastrointestinal (GI) illness that could affect oral absorption of brigatinib in the opinion of the treating Investigator are not eligible * Patients with recent history of pulmonary embolism, or untreated deep vein thrombosis in the last 3 months are not eligible * Note: Patients may be eligible if they have received at least 3 months of anticoagulation for a deep vein thrombosis * Patients who have a known or suspected hypersensitivity to brigatinib, or its excipients are not eligible * Patients who have received systemic treatment with strong cytochrome P-450 (CYP)3A inhibitors, strong CYP3A inducers or moderate CYP3A inducers within 14 days before registration are not eligible