Experimental drug targets rare thymus cancers after chemotherapy fails

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

* IINCLUSION CRITERIA: * Participants must have histologically confirmed (by the pathology department/CCR/NCI) thymoma or thymic carcinoma. * Participants must have had at least one prior line of platinum-based chemotherapy. Progressive disease must be documented prior to study entry and participants must have advanced, unresectable disease that is not amenable to surgical resection. * Disease must be measurable with at least 1 unidimensional measurable lesion by RECIST1.1. * Participants must be aged \>=18 years. * ECOG performance status \<=1. * Participants must have adequate organ and marrow function as defined below: * absolute neutrophil count: \>= 1,500/mm\^3 OR \>= 1.5 x 10\^9/L * platelets: \>=\> 100,000/mm\^3 OR \>= 100 x 10\^9/L * hemoglobin: \>= 9g/dL (may have been transfused) * total bilirubin: \<= the upper limit of normal range (ULN) OR \<= 3.0 x ULN for participants with documented metastatic disease to the liver * AST(SGOT)/ALT(SGPT): \<= 1.5 x ULN OR \<= 5 x ULN for participants with documented metastatic disease to the liver * ALP: \<= 2.5 x ULN * creatinine clearance: \>= 60 mL/min/1.73 m\^2 calculated by calculated using eGRF in the clinical lab * INR: normal INR, per institutional guidelines * PT: \<= 1.5 x ULN * aPTT: \<= 1.5 x ULN * Negative serum or urine pregnancy test at screening for individuals of childbearing potential (IOCBP). NOTE: IOCBP is defined as any individual who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal. If necessary, to confirm postmenopausal status an FSH level will be included at screening. The effects of Bintrafusp alfa on the developing human fetus are unknown. For this reason, individuals of childbearing potential and those that can father children must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for at least 2 months after the last dose of the drug. * Participants with previously treated brain or CNS metastases are eligible provided that the participant has recovered from any acute side effects of radiotherapy and does not require treatment with steroids, and any whole brain radiation therapy was completed at least 2 weeks prior to enrollment. * Ability of participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * History of allergic reactions attributed to compounds of similar chemical or biologic composition to bintrafusp alfa. * History of anaphylaxis or recent (within 5 months) history of uncontrollable asthma. * Prior treatment with PD-1 or PD-L1-directed immune checkpoint blockade is not permitted. Prior treatment with other immunomodulating drugs such as cancer vaccines is permitted based on investigators' discretion as long as treatment was not discontinued due to life-threatening adverse events (laboratory abnormalities alone with prior therapy will not exclude participants from this trial). * Concurrent treatment with a non-permitted drug * Prior anticancer treatment within 14 days before treatment (e.g., cytoreductive therapy, radiotherapy \[with the exception of palliative bone directed radiotherapy\], immune therapy, or cytokine therapy except for erythropoietin); major surgery within 14 days before treatment (excluding prior diagnostic biopsy); prior systemic therapy (or 5 half-lives of a drug, whichever is shorter) with immunosuppressive agents within 14 days before treatment; use of hormonal agents for anti-cancer therapy within 7 days before treatment; or use of any investigational drug within 14 days before treatment. Note: Participants receiving bisphosphonate or denosumab are eligible provided treatment was initiated at least 14 days before treatment. * History of previous malignant disease within the last 3 years with the following exceptions: basal or squamous cell carcinoma in situ of the skin treated with curative intent, endoscopically resected GI cancers limited to the mucosal layer without recurrence in \> 1 year, cervical carcinoma in situ, ductal carcinoma in situ of the breast, papillary or follicular thyroid carcinoma, and superficial/non-muscle invasive bladder cancer. * Active brain or CNS metastases causing clinical symptoms or metastases that require therapeutic intervention. * Active or history of autoimmune disease that might deteriorate when receiving an immune-stimulatory agent, with the exception of diabetes type I, vitiligo, psoriasis, autoimmune thyroid disease not requiring immunosuppressive treatment, or pure red cell aplasia that are adequately managed with medical therapy. In addition, anti-acetylcholine receptor binding antibodies will be checked during screening and participants will be ineligible if results are positive, even if there is no clinical history of autoimmune disease. * Participants receiving systemic corticosteroids at doses \> 10 mg daily prednisone equivalent will be excluded. However, participants on inhaled steroids and adrenal replacement steroid doses up to 10 mg daily prednisone equivalents are permitted in the absence of autoimmune disease * Active infection requiring systemic therapy or significant acute or chronic infections including, among others: * Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening test positive). * Known history of testing positive for HIV or testing positive for HIV at screening or known acquired immunodeficiency syndrome. HIV-positive TET participants are ineligible because of the risk of developing opportunistic infections after treatment with an immune checkpoint inhibitor. Additionally, TET participants are at higher risk of developing opportunistic infections due to underlying immune defects. Prior cases of disseminated herpes virus, cytomegalovirus and fungal infections have been documented in this patient population. * Prior organ transplantation including allogenic stem-cell transplantation, Participants who have had prior transplants that do not require immunosuppression are eligible. * Persisting toxicity related to prior therapy (NCI CTCAE v. 5 Grade \> 1); however, alopecia, sensory neuropathy Grade \<= 2, or other Grade \<= 2 not constituting a safety risk based on investigator's judgment are acceptable. * Participants unwilling to accept blood products as medically indicated. * Pregnant or lactating individuals. Pregnant individuals are excluded from this study because Bintrafusp alfa is in the class of agents known as antineoplastics/monoclonal antibodies with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Bintrafusp alfa, breastfeeding should be discontinued if the mother is treated with Bintrafusp alfa. * Known alcohol or drug abuse. * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, cerebral vascular accident/stroke \< 6 months prior to enrollment, myocardial infarction \< 6 months prior to enrollment, or psychiatric illness/social situations that would limit compliance with study requirements. All other severe acute or chronic medical conditions including immune colitis, inflammatory bowel disease, immune pneumonitis, drug-induced pneumonitis requiring oral or IV steroids, interstitial lung disease, pulmonary fibrosis or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the individual inappropriate for entry into this study. Participants with history of bleeding diathesis or recent major bleeding events considered by the Investigator as high risk for investigational drug treatment are also excluded. * Administration of live vaccine within 4 weeks prior to treatment, with the exception of vaccination against COVID-19