Aerosolized Azacytidine as Epigenetic Priming for Bintrafusp Alfa-Mediated Immune Checkpoint Blockade in Patients With Unresectable Pulmonary Metastases From Sarcomas, Germ Cell Tumors, or Epithelial Malignancies

* INCLUSION CRITERIA: 1. Histologically or cytologically confirmed, unresectable pulmonary metastases from sarcomas, melanomas, germ cell tumors, or epithelial malignancies excluding lung and renal cell carcinomas. 2. Patients with extrathoracic disease may be eligible provided there are 5 or fewer low volume non-thoracic sites (less than or equal to 3 cm/nodule) that are not life-threatening and are potentially treatable with metastasis-directed therapy whether they are symptomatic or not. 3. Patients with bone metastases (less than 5 sites) are potentially eligible for study. 4. Patients must have received first line standard of care systemic treatment for their malignancies. 5. Patients with tumors with potentially actionable mutations are eligible for study if their metastases are refractory to approved first-line targeted agents. 6. Patient's PD-L1 expression in cancer cells may be positive or negative as quantitated by immunohistochemistry techniques. 7. Patients must have measurable disease per RECIST 1.1. 8. Patient's pulmonary disease can be safely accessed via bronchoscopic, thoracoscopic or transthoracic percutaneous biopsy, and patient must be willing to undergo biopsy as well as bronchoscopy before and after treatment. 9. Age greater than or equal to 18 years. Because no dosing or adverse event data are currently available on the use of aerosolized AZA in patients \< 18 years of age, children are excluded from this study, but may be eligible for future pediatric trials. 10. ECOG performance status of less than or equal to 1 11. Patients must be without evidence of unstable or decompensated myocardial disease, and have adequate pulmonary reserve evidenced by FEV1 and adjusted DLCO greater than or equal to 60% predicted and FEV1/FVC ratio greater than or equal to 60%; pCO2 less than or equal to 45 and pO2 greater than ir equal to 60 on room air. 12. Normal organ and marrow function as defined below: * leukocytes greater than or equal to 3,000/mcL * absolute neutrophil count greater than or equal to 1,500/mcL (without transfusion or cytokine support) * absolute lymphocyte count \> 800/mcL * platelets greater than or equal to 100,000/mcL * Hgb greater than or equal to 9 g/ dL * PT no more than 2 seconds above the ULN * total bilirubin \< 1.5 X institutional upper limit of normal OR * direct bilirubin less than or equal to ULN for patients with total bilirubin \> 1.5 ULN * serum albumin greater than or equal to 2.0 mg/dL * AST(SGOT)/ALT(SGPT) less than or equal to 1.5 X institutional ULN * ALP less than or equal to 2.5 X institutional ULN * creatinine less than or equal to 1.6 mg/mL OR --creatinine clearance (eGFR) greater than or equal to 30 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal at the time AZA and M7824 treatment commences. 13. Patients with history of brain metastases except those with meningeal carcinomatosis or leptomeningeal disease may be eligible for treatment a minimum of 2 weeks following completion of gamma knife or whole brain radiotherapy, or 4 weeks following surgical resection of brain metastasis; provided post-treatment MR scan reveals no evidence of active disease, and no ongoing need for systemic steroids. 14. The effects of AZA and Bintrafusp alfa on the developing human fetus are unknown. For this reason and because the agents used in this trial are known to be teratogenic, women of child-bearing potential and men 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 125 days following the last dose of Bintrafusp alfa for males, and 65 days following the last dose of Bintrafusp alfa for females. 15. Ability of subject to understand and the willingness to sign a written informed consent document. 16. Ability of subject and the willingness to co-enroll and sign a written informed consent document for 06C0014 "Prospective Evaluation of Genetic and Epigenetic Alterations in Patients with Thoracic Malignancies". EXCLUSION CRITERIA: 1. Patients with cancers harboring mutations targetable with approved agents who have not progressed on targeted therapy. 2. Patients with primary lung cancers are excluded from study due to potential exacerbation of pulmonary toxicities from investigational therapy due to evolution or treatment of their malignancies. 3. Patients with renal cancers are excluded from study due to potential bleeding from these highly vascular metastases. 4. Active smokers 5. Patients either receiving systemic steroids other than physiologic replacement doses, or inhaled corticosteroids. 6. Previous treatment with targeted therapy, immune checkpoint inhibitor, DNA demethylating agent, systemic chemotherapy, or radiation therapy to an index lesion within three weeks prior to starting protocol therapy. Patients with prior treatment with immune checkpoint inhibitors, and DNA demethylating agents may be eligible for study provided more than three weeks have elapsed since treatment and they did not experience serious immune adverse events that required discontinuation of the immune checkpoint inhibitor. 7. History of allergic reactions attributed to compounds of chemical or biologic composition similar to Bintrafusp alfa and AZA. 8. Clinically significant cardiovascular / cerebrovascular disease as follows: cerebral vascular accident / stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification Class greater than or equal to II), serious cardiac arrhythmia, clinically significant bleeding or clinically significant pulmonary embolism. 9. History of pneumonitis (idiopathic or drug induced) unless cleared by pulmonary consultants. 10. Receipt of any organ transplantation, including allogeneic stem-cell transplantation, except for transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). 11. Active Hepatitis A, Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). 12. Human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness due to unknown effects of AZA on systemic immunity. 13. Other active infection requiring systemic therapy, including COVID-19 (testing will be required as part of screening). 14. Pregnant women are excluded from this study because AZA and Bintrafusp alfa may have 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 and AZA, breastfeeding should be discontinued if the mother is treated with Bintrafusp alfa and AZA. 15. Other severe acute or chronic medical condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the investigator would make the patient inappropriate for entry into this study. 16. Recent major bleeding events considered by the Investigator as high risk for investigational drug treatment. 17. Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent with the exceptions: * Diabetes type I, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment; * Subjects requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for the purpose of hormonal replacement and at doses less than or equal to 10 mg of prednisone or equivalent per day; * Administration of steroids for other conditions through a route known to result in a minimal systemic exposure (topical, intranasal, intro-ocular, or intra-articular). 18. Patients receiving another investigational agent. 19. An additional malignancy that is progressing or requires active treatment. 20. Administration of live vaccines with 30 days prior to enrollment. Administration of inactivated vaccines (e.g., inactivated influenza vaccines) is permitted during the study. 21. Subjects unwilling to accept blood products as medically indicated. 22. Emotional, psychiatric or substance abuse disorders that would interfere with cooperation with the requirements and safety of the trial.