Testing Atezolizumab With Selinexor in People ≥ 12 Years Old With Alveolar Soft Part Sarcoma, The AXIOM Trial

Inclusion Criteria: * To be enrolled in the safety run-in, patients must have an advanced soft tissue sarcoma (not otherwise specified \[NOS\]). To be enrolled in the ASPS cohort, patients must have histologically or cytologically confirmed alveolar soft part sarcoma that is not curable by surgery * 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 CT scan, MRI, or calipers by clinical exam. * Patients with unresectable, metastatic and measurable ASPS that is resistant/refractory to ICI treatment will be eligible for the ASPS cohort of this study if they show clinical and/or radiological evidence of disease progression after receiving prior ICI therapy (including history and increasing physical symptoms). On-study documentation will include a physician's rationale that supports evidence of clinical disease progression (i.e., increasing tumor pain) * Age \>= 12 years. Because no dosing or adverse event data are currently available on the use of atezolizumab in combination with selinexor in patients ˂ 18 years of age, children \< 12 years of age are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 70%) * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9…