Durvalumab and Epacadostat for Treatment of Unresectable, Recurrent, or Metastatic Epstein-Barr Virus Positive Nasopharyngeal Cancer

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Life expectancy of at least 4 months * Patient is capable of giving signed informed consent and is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Body weight \> 40 kilograms (kg) * Patients must have a histological or cytological diagnosis of Epstein-Barr virus positive (EBV+) nasopharyngeal carcinoma that is not amenable to curative intent therapy (i.e. surgical resection, locoregional radiation therapy, concurrent chemoradiation) * Patients must decline, be ineligible or intolerant to at least 1 standard treatment regimen in the advanced or metastatic setting, if such a therapy exists * Patients must have disease progression within 6 months of completion of platinum-based concurrent chemoradiation or after platinum-based chemotherapy administered for the treatment of recurrent or metastatic disease * If patient has known brain metastases, they must have stable neurologic status for at least 4 weeks without the use of steroids or on stable or decreasing dose of =\< 10 mg daily prednisone (or equivalent), and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events (AEs) (patients with a history of carcinomatous meningitis are not eligible) * Patients may have had prior chemotherapy or immunotherapy or radiation therapy. Patients should discontinue prior medical therapy at least 5 drug half-lives or 28 days prior to the first dose of treatment on study (whichever is shorter). Patients should complete any prior radiation therapy at least 14 days prior to the initiation of treatment on study. Also, any drug related adverse events identified during prior therapy must be well controlled (typically resolution to =\< grade 1, OR resolved upon investigator review prior to initiation of this therapy * No systemic antineoplastic therapy may be received by the patient between the time of the biopsy and the first administration of study treatment * Patient must agree to any protocol mandated biopsies of tumor (deemed accessible, safe and appropriate for biopsy by the investigator?s assessment) and they must allow acquired tissue to be used for biomarker and immunological analysis * For women of childbearing potential, negative serum or urine pregnancy test within 14 days to the first epacadostat, or durvalumab and use of birth control from 30 days prior to the first administration of treatment on study and 120 days following last day administration of treatment on study * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy) * Women \>= 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \> 1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy) * Male patients must be surgically sterile, or must agree to use contraception during the study and at least 120 days following the last day of study drug administration Exclusion Criteria: * Active autoimmune disease that has required systemic treatment in past 2 years. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], systemic lupus erythematosus, sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, rheumatoid arthritis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome or treated Graves disease) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Patients with celiac disease controlled by diet alone * Congestive heart failure (New York Heart Association class III to IV) * History or presence of an abnormal electrocardiogram (ECG) that, in the investigator's opinion, is clinically meaningful. Screening corrected QT (QTc) interval \> 470 milliseconds is excluded. In the event that a single QTc is \> 470 milliseconds, the subject may enroll if the average QTc for the 3 ECGs is \< 470 milliseconds. For subjects with an intraventricular conduction delay (QRS interval \> 120 milliseconds), the corrected JT (JTc) interval may be used in place of the QTc with sponsor approval. The JTc must be \< 340 milliseconds if JTc is used in place of the QTc. Subjects with left bundle branch block are excluded * Uncontrolled or clinically significant conduction abnormalities (e.g., ventricular tachycardia on anti-arrhythmics are excluded), 1st degree atrioventricular (AV) block or asymptomatic left anterior fascicular block (LAFB)/right bundle branch block (RBBB) are eligible * Uncontrolled, symptomatic ischemia within 6 months of first dose of study treatment or known myocardial infarction in the previous six months * Evidence of interstitial lung disease or any history of autoimmune pneumonitis including symptomatic and/or pneumonitis requiring treatment * Infectious * Evidence of significant active infection (e.g., pneumonia, cellulitis, wound abscess, etc.) requiring systemic therapy at time of study enrollment * Active hepatitis B (hepatitis B surface antigen \[HBsAg\] reactive) associated the aspartate aminotransferase (AST) or alanine aminotransferase (ALT) elevations \> 1.5 x upper limit of normal (ULN). Patients who are HBsAg reactive must be on appropriate antiviral therapy while receiving treatment on study * Hepatitis C (hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Presence of a gastrointestinal condition that may affect drug absorption. Administration of epacadostat through a feeding tube is permitted * Any other current or previous malignancy within the past 2 years that, in the opinion of the principal investigator will interfere with study-specific endpoints * Any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria * Patients with grade \>= 2 neuropathy will be evaluated on a case-by-case basis after consultation with the study physician * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the study physician * History of leptomeningeal carcinomatosis * Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis (TB) testing in line with local practice) * Hepatitis B ? Half of NPC patients have been infected with hepatitis B (Cancer Epidemol Biomarkers Prev. 2015. 24:1766-73, N = 711) and, therefore, inclusion of healthy patients with a history of hepatitis B is a central part of this study. In addition, PD-1 antibodies have been proven to be safe in patients with active hepatitis and hepatocellular carcinoma (e. g. KEYNOTE 224). However, patients with hepatitis B virus (HBV) surface antigen positive (HBSAg) must have AST and total bilirubin \< 1.5 x ULN AND * Negative HBV RNA polymerase chain reaction (PCR) OR * On antivirals for HBV AND at least 8 weeks of prior anti-PD1 antibody therapy AND no history of AST or total bilirubin levels \> 1.5 x ULN due to PD-1 antibody therapy * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA * Known human immunodeficiency virus (HIV) (positive HIV 1/2 antibodies) ? Consistent with current guidelines from the NCI / Cancer Therapy Evaluation Program (CTEP), ?HIV infected patients on effective antiretroviral therapy with undetectable viral load within 6 months are eligible for this trial? (CTEP protocol template) * Intercurrent illness not otherwise specified * Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent * Patients receiving systemic steroid therapy for a chronic inflammatory condition. Topical steroids, nasal and inhaled steroids are permitted. Prednisone or equivalent =\< 10 mg/day is permitted as hormone replacement; higher dosage prednisone should be stopped at least 14 days prior to cycle 1 day 1 (c1d1) * Subjects receiving monoamine oxidase inhibitors (MAOIs) or drug which has significant MAOI activity (meperidine, linezolid, methylene blue) within the 21 days before screening * Any history of serotonin syndrome (SS) after receiving serotonergic drugs * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients * Receipt of live attenuated vaccine within 30 days before the first dose of study treatment. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, chicken pox, yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed * Current or prior use of immunosuppressive medication within 14 days (use 28 days if combining durvalumab with a novel agent) before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) * Systemic corticosteroids at physiologic doses not to exceed \<\<10 mg/day\>\> of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography \[CT\] scan premedication) * Absolute neutrophil count (ANC) \< 1.0 x 10\^9/L * Platelets \< 75 x 10\^9/L * Hemoglobin \< 9 g/dL or \< 5.6 mmol/L (transfusion is acceptable to meet this criterion) * Serum creatinine \>= 1.5 x institutional upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate can also be used in place of creatinine or creatinine clearance (CrCl)) \< 50 mg/min for subjects with creatinine levels \> 1.5 x institutional ULN * AST or ALT \> 2.5 x institutional ULN * Alkaline phosphatase \> 2.5 x ULN * Note: Subjects with 1) bone metastases and gamma-glutamyl transpeptidase (GGT) \< 2.5 x ULN may enroll if the alkaline phosphatase is \< 5 x ULN * Total bilirubin above 1.5 x the institutional ULN AND conjugated bilirubin \>= 2.0 x ULN * International normalized ratio (INR) or prothrombin time (PT) \> 1.5 x ULN * Activated partial thromboplastin time (aPTT) \> 1.5 x ULN