• Age \>= 18 years

• Histological or cytological confirmation of adenocarcinoma of the stomach or gastroesophageal junction

• Have locally advanced unresectable or metastatic disease that has progressed =\< 180 days since last treatment

• One or more measurable or nonmeasurable evaluable lesions per Response Evaluation Criteria in Solid Tumors (RECIST)

• Planned for second line treatment defined by failing or were intolerant to previous standard chemotherapies containing one or more of the following agents:

‣ Fluoropyrimidine (IV 5-FU or capecitabine) and platinum (cisplatin or oxaliplatin)

⁃ Trastuzumab in case of HER2-positive disease

⁃ NOTE: For the patients whose disease recurred =\< 168 days from the last dose of adjuvant anticancer chemotherapy, that adjuvant anticancer chemotherapy is counted as 1 prior chemotherapy line

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1

• Ability to swallow oral medications

• Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 7 days prior to registration)

• Platelet count \>= 100,000/mm\^3 (obtained =\< 7 days prior to registration)

• Hemoglobin \>= 9.0 g/dL (obtained =\< 7 days prior to registration)

• Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 7 days prior to registration)

• Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3 x ULN ( =\< 5.0 x UNL, if with liver metastasis) (obtained =\< 7 days prior to registration)

• International normalized ratio (INR) =\< 1.5 x ULN, and a partial thromboplastin time (PTT) =\< 5 seconds above the ULN (unless receiving anticoagulation therapy) (obtained =\< 7 days prior to registration)

‣ Note: Patients receiving warfarin must be switched to low molecular weight heparin and have achieved stable coagulation profile prior to first dose of protocol therapy

⁃ Note: Patients on full-dose anticoagulation must be on a stable dose (minimum duration 14 days) of oral anticoagulant or low molecular weight heparin (LMWH)

⁃ Exception: If receiving warfarin, the patient must have an INR =\< 3.0. For heparin and LMWH there should be 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)

• Urinary protein is =\< 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 to allow participation in this protocol) (obtained =\< 7 days prior to registration)

• Creatinine =\< 1.5 times the ULN or creatinine clearance (measured via 24-hour urine collection) \>= 50 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) (obtained =\< 7 days prior to registration)

• Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only

• Ability to complete questionnaire(s) by themselves or with assistance

• Provide informed written consent =\< 28 days prior to registration

• Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study)

• Because the teratogenicity of ramucirumab is not known, the patient, if sexually active, must be postmenopausal, surgically sterile, or using effective contraception (hormonal or barrier methods)