This phase I/II trial studies how well tiragolumab and atezolizumab works when given to children and adults with SMARCB1 or SMARCA4 deficient tumors that that has either come back (relapsed) or does not respond to therapy (refractory). SMARCB1 or SMARCA4 deficiency means that tumor cells are missing the SMARCB1 and SMARCA4 genes, seen with some aggressive cancers that are typically hard to treat. Immunotherapy with monoclonal antibodies, such as tiragolumab and atezolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread.

Severe Aplastic Anemia (SAA) is a rare condition in which the body stops producing enough new
blood cells. SAA can be cured with immune suppressive therapy or a bone marrow transplant.
Regular treatment for patients with aplastic anemia who have a matched sibling (brother or
sister), or family donor is a bone marrow transplant. Patients without a matched family donor
normally are treated with immune suppressive therapy (IST). Match unrelated donor (URD) bone
marrow transplant (BMT) is used as a secondary treatment in patients who did not get better
with IST, had their disease come back, or a new worse disease replaced it (like leukemia).

This trial will compare time from randomization to failure of treatment or death from any
cause of IST versus URD BMT when used as initial therapy to treat SAA.

The trial will also assess whether health-related quality of life and early markers of
fertility differ between those randomized to URD BMT or IST, as well as assess the presence
of marrow failure-related genes and presence of gene mutations associated with MDS or
leukemia and the change in gene signatures after treatment in both study arms.

This study treatment does not include any investigational drugs. The medicines and procedures
in this study are standard for treatment of SAA.