Berzosertib and Irinotecan in Treating Patients With Progressive, Metastatic, or Unresectable TP53 Mutant Gastric or Gastroesophageal Junction Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed progressive metastatic or unresectable gastric or GEJ adenocarcinoma. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam. * Patients must have progressed after or been intolerant of at least two lines of systemic therapy. Patients with HER2 positive gastric and GEJ adenocarcinoma must have progressed on trastuzumab plus chemotherapy in the first line setting. Patients with microsatellite unstable (MSI-H) tumors must have received prior immunotherapy with pembrolizumab. * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of M6620 in combination with irinotecan in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * Both men and women of all races and ethnic groups are eligible for this trial. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 60%). * Leukocytes \>= 3,000/mcL. * Absolute neutrophil count \>= 1,500/mcL. * Platelets \>= 100,000/mcL. * Hemoglobin \>= 9 g/dL. * Total bilirubin within normal institutional limits. * A…