Viral Oncoprotein Targeted Autologous T Cell Therapy for Merkel Cell Carcinoma

Inclusion Criteria: * Histopathological documentation of MCC concurrent with the diagnosis of metastatic disease * Evidence of MCPyV TAg tumor expression * Available peptide-MHC pair that can be folded into a tetramer for which MCPyV TAg-specific cells can be generated and reactivity to cell lines expressing MCPyV TAg with the corresponding human leukocyte antigen (HLA) * Bi-dimensionally measurable disease by palpation, clinical exam, or radiographic imaging (x-ray, computed tomography \[CT\] scan, positron emission tomography \[PET\] scan, magnetic resonance imaging \[MRI\], or ultrasound) * At least 3 weeks must have passed since any of the following: systemic corticosteroids, immunotherapy (for example, interleukins, MCC vaccines, intravenous immunoglobulin, expanded polyclonal tumor infiltrating lymphocyte \[TIL\] or lymphokine-activated killer \[LAK\] therapy), pentoxifylline, other small molecule or chemotherapy cancer treatment, other investigational agents or other agents that target merkel cell carcinoma * Cardiac ejection fraction \>= 40% (multigated acquisition \[MUGA\] or echocardiogram); for patients with significant risk factors for coronary artery disease (CAD) (including family history, hypertension, and/or dyslipidemia), or age \> 50, stress echo or stress thallium testing is required Exclusion Criteria: * Unable to generate antigen-specific MCPyV TAg-specific CD8+ T cells for infusions * Active infections prior to receiving study treatment or systemic infection requiring chronic maintenance or suppressive therapy * Eastern Cooperative Oncology Group (ECOG) performance status \> 2 * White blood cell (WBC) \< 2000/mcl * Hemoglobin (Hb) \< 8 g/dL * Absolute neutrophil count (ANC) \< 1000/mcl * Platelets \< 50,000/mcl * New York Heart Association functional class III-IV heart failure, symptomatic pericardial effusion, stable or unstable angina, symptoms of coronary artery disease, congestive heart failure, clinically significant hypotension, or an ejection fraction of =\< 40 % (echocardiogram or MUGA) * Clinically significant pulmonary dysfunction, as determined by medical history and physical exam; patients so identified will undergo pulmonary functions testing and those with forced expiratory volume in one second (FEV1) \< 2.0 L or diffusing capacity of the lung for carbon monoxide (DLCO) (corrected for hemoglobin \[Hgb\]) \< 50% will be excluded * Creatinine clearance \< 30 ml/min which cannot be attributed to MCC metastasis * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) \> 5 x upper limit of normal (ULN) * Bilirubin \> 3 x ULN which cannot be attributed to MCC metastasis * Active autoimmune disease (e.g. systemic lupus erythematosus, vasculitis, infiltrating lung disease, inflammatory bowel disease) whose possible progression during treatment would be considered unacceptable by the investigators * Symptomatic and untreated central nervous system (CNS) metastasis; however, patients with 1-2 asymptomatic, less than 1 cm brain/CNS metastases without significant edema may be considered for treatment; if sub-centimeter CNS lesions are noted at study entry, then a repeat imaging will be performed if more than 4 weeks have elapsed from the last scan * Any condition or organ toxicity that is deemed by the principal investigator (PI) or the attending physician to place the patient at unacceptable risk for treatment on the protocol * Pregnant women, nursing mothers, men or women of reproductive ability who are unwilling to use effective contraception or abstinence; women of childbearing potential must have a negative pregnancy test within two weeks prior to entry * Clinically significant and ongoing immune suppression including, but not limited to, systemic immunosuppressive agents such as cyclosporine or corticosteroids, chronic lymphocytic leukemia (CLL), uncontrolled human immunodeficiency virus (HIV) infection, or solid organ transplantation * Patients may not be on any other treatments for their cancer aside from those included in the protocol; patients may not undergo another form of treatment concurrently with this study