Pembrolizumab in Treating Participants With Unresectable Thymoma or Thymic Cancer

Inclusion Criteria: * Unresectable thymoma or thymic carcinoma. * Any line of prior therapy allowed. * Be willing and able to provide written informed consent/assent for the trial. * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on day 1. Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen. * Have a performance status (PS) of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) PS. * No history of or current diagnosis of a 'significant autoimmune disease" or paraneoplastic autoimmune disease, i.e. myasthenia gravis, Lambert-Eaton, systemic lupus, rheumatoid arthritis. For minor 'autoimmune' disorders such as psoriasis, arthritis (not including rheumatoid arthritis), Raynaud's disease; these are allowed onto trial. * No active hepatitis or diagnosis of human immunodeficiency virus (HIV) disease. * No prior malignancy unless it was cured over 2 years ago; i.e. prostate cancer, or early stage (I-III) solid tumors. Patients with a prior basal skin cancer or squamous cell carcinoma of the skin or in situ cervical malignancy that have undergone curative treatment are excluded from this requirement. * Absolute neutrophil count \>= 1500/mcL (within 10 days of treatment initiation). * Platelets \>= 100000mcL (within 10 days of treatment initiation). * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) (within 10 days of treatment initiation). * Serum creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (within 10 days of treatment initiation). Note: Creatinine clearance should be calculated per institutional standard. * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (within 10 days of treatment initiation). * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases (within 10 days of treatment initiation). * Albumin \>= 2.5 mg/dL (within 10 days of treatment initiation). * International normalized ratio (INR) or prothrombin time (PT) activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (within 10 days of treatment initiation). * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female subjects of childbearing potential must be willing to use an adequate method of contraception, for the course of the study through 120 days after the last dose of study medication. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Male subjects of childbearing potential must agree to use an adequate method of contraception, starting with the first dose of study therapy through 120 days after the last dose of study therapy. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Has a known history of active TB (Bacillus tuberculosis). * Hypersensitivity to pembrolizumab or any of its excipients. * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent. - Note: Subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study. - Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using