Ramucirumab and Trifluridine/Tipiracil or Paclitaxel for the Treatment of Patients With Previously Treated Advanced Gastric or Gastroesophageal Junction Cancer

Inclusion Criteria: * 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 …