Carboplatin and Paclitaxel With or Without Ramucirumab in Treating Patients With Locally Advanced, Recurrent, or Metastatic Thymic Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed thymic carcinoma; thymic carcinoma may be defined as "thymic epithelial malignancy, consistent with thymic carcinoma", or "World Health Organization (WHO) type C thymic epithelial tumor", or "thymic epithelial malignancy" with radiographic imaging consistent with thymic carcinoma * Patients must have unresectable thymic carcinoma, that is either locally advanced, recurrent, or metastatic * Patients must not be candidates for localized surgery * Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI) within 28 calendar days prior to randomization; the CT from a combined positron emission tomography (PET)/CT may be used only if it is of diagnostic quality; non-measurable disease must be assessed within 42 calendar days prior to randomization; all known sites of disease must be assessed and documented on the baseline tumor assessment form (Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1) * Patients must have a Zubrod performance status of 0 to 2 * Patients must not have undergone major surgery within 28 calendar days prior to randomization, or minor surgery/subcutaneous venous access device placement within 7 calendar days prior to randomization; the patient must not have elective or planned major surgery to be performed during the course of the clinical trial * Patients must not have had prior systemic anti-cancer therapy for locally advanced or metastatic unresectable thymic carcinoma * If patients have recurrent unresectable thymic carcinoma, patients may have had prior neoadjuvant or adjuvant chemotherapy if treatment concluded \>= 6 months prior to randomization * Patients must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 calendar days prior to registration; patient must not have brain metastases unless: (1) metastases have been treated and have remained controlled for at least two weeks following treatment, AND (2) patient has no residual neurological dysfunction off corticosteroids for at least 1 day * Patients must not be candidates for radiation therapy with curative intent; prior palliative radiation therapy is allowed as long as a period of 7 days has passed since the last dose was received and the patient has recovered from any associated toxicity at the time of randomization * Absolute neutrophil count (ANC) \>= 1500/mcL documented within 28 calendar days prior to randomization * Hemoglobin \>= 9 g/dL (5.58 mmol/L) documented within 28 calendar days prior to randomization * Platelets \>= 100,000/mcL documented within 28 calendar days prior to randomization * International normalized ratio (INR) =\< 1.5 documented within 28 calendar days prior to randomization * Partial thromboplastin time (PTT) =\< 5 seconds above the institutional upper limit of normal (IULN) (unless receiving anticoagulation therapy) documented within 28 calendar days prior to randomization * Patients receiving warfarin must be switched to low molecular weight heparin and have achieved stable coagulation profile 14 days prior to randomization * Patients must not have experienced any grade 3 or above gastrointestinal (GI) bleeding within 84 calendar days prior to randomization * Patients must not have a history of deep vein thrombosis (DVT), pulmonary embolism (PE), or any other significant thromboembolism (venous port or catheter thrombosis or superficial venous thrombosis are not considered "significant") during the 84 calendar days prior to randomization * Total bilirubin =\< 1.5 x the institutional upper limit normal (IULN) documented within 28 calendar days prior to randomization * Aspartate aminotransferase (aspartate transaminase \[AST\]) and alanine aminotransferase (alanine transaminase \[ALT\]) =\< 3.0 x IULN; for patients with liver metastases, total bilirubin and AST or ALT must be =\< 5.0 x IULN documented within 28 calendar days prior to randomization * Patients must not have any of following: * Cirrhosis at a level of Child-Pugh B (or worse) * 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 x IULN, or creatinine clearance (measured via 24-hour urine collection) \>= 40 mL/minute (that is, if serum creatinine is \> 1.5 x ULN, a 24-hour urine collection to calculate creatinine clearance must be performed) documented within 28 calendar days prior to randomization * Patient urinary protein must be =\< 1+ on dipstick or routine urinalysis (UA); if urine dipstick or routine analysis is \>= 2+, a 24-hour urine collection for protein must demonstrate \< 1000 mg of protein in 24 hours); these tests must be documented within 28 calendar days prior to randomization * Patients must not have 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 randomization * Patients must not have a history of uncontrolled or poorly-controlled hypertension (defined as \> 160 mmHg systolic or \> 100 mmHg diastolic for \> 4 weeks) despite standard medical management * Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method (hormonal or barrier method of birth control; abstinence) prior to randomization, during the study participation and for 4 months after the last dose of protocol treatment; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Patients must not have experienced hemoptysis (defined as bright red blood or \>= 1/2 teaspoon) within 2 months prior to randomization or with radiographic evidence of intratumor cavitation or has radiologically documented evidence of major blood vessel invasion or encasement by cancer * Patients must not have a prior history of gastrointestinal perforation/fistula (within 6 months of randomization) or risk factors for perforation * Patients must not have a serious or nonhealing wound, ulcer, or bone fracture within 28 calendar days prior to randomization * Patients must not be receiving chronic antiplatelet therapy, including aspirin, nonsteroidal anti-inflammatory drugs (NSAIDs, including ibuprofen, naproxen, and others), dipyridamole or clopidogrel, or similar agents within 7 days prior to randomization; once-daily aspirin use (maximum dose 325 mg/day) is permitted * Patients must be offered the opportunity to participate in banking of specimens for future research * Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system