Durvalumab in Treating Patients With Primary, Post-Polycythemia Vera, or Post-Essential Thrombocythemia Myelofibrosis

Inclusion Criteria:

* Patients must have a histologically confirmed diagnosis of primary myelofibrosis (PMF), post-polycythemia vera (post-PV) myelofibrosis (MF), or post-essential thrombocythemia (post-ET) MF using World Health Organization Criteria
* Patients must have disease that requires therapy, including intermediate-1, intermediate-2, or high-risk disease according to the International Prognostic Scoring System (IPSS) or Dynamic-IPSS
* Patients must be resistant to, intolerant of, or ineligible for Janus kinase (JAK)2 inhibitor therapy, or have refused such therapy
* Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
* Patients must have adequate organ and bone marrow function within 14 days prior to registration, as defined below:
* Absolute neutrophil count \>= 1.0 x 10\^9/L
* Platelets \>= 75 x 10\^9/L
* Total bilirubin =\< institutional upper limit of normal (ULN) (or =\< 3 X ULN if Gilbert's syndrome present or if bilirubin increase related to MF)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase\[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SPGT\]) =\< 2.5 X institutional ULN
* Creatinine clearance \>= 50 mL/min/1.73 m\^2 (calculated by estimated glomerular filtration rate \[eGFR\] from EPIC)
* Female subjects who are pregnant or breast-feeding are not eligible; should a female patient become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; likewise, should a female partner of a male patient become pregnant or suspect she is pregnant while participating in the study, he should inform his treating physician and the female partner should call her physician immediately
* Female of child bearing potential (FOCBP) must have a negative pregnancy test (serum or urine) within 7 days prior to registration on study; NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:

  * Has not undergone a hysterectomy or bilateral oophorectomy
  * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months)
* Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study

Exclusion Criteria:

* Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis, Crohn's disease\], diverticulitis with the exception of a prior episode that has resolved or diverticulosis, celiac disease, irritable bowel disease, or other serious gastrointestinal chronic conditions associated with diarrhea; systemic lupus erythematosus; Wegener's syndrome \[granulomatosis with polyangiitis\]; myasthenia gravis; Graves' disease; rheumatoid arthritis; hypophysitis, uveitis; etc.) within the past 3 years prior to the start of treatment

  * The following are exceptions to this criterion: subjects with vitiligo or alopecia; subjects with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement; or subjects with psoriasis not requiring systemic treatment
* Known human immunodeficiency virus (HIV), hepatitis C virus (HCV) or evidence of active hepatitis B virus (HBV)
* Current or prior use of immunosuppressive medication within 14 days prior to first dose of durvalumab; the following are exceptions to this criterion: intranasal, inhaled, topical or local steroid injections (eg. intra-articular injection); steroids as premedication for hypersensitivity reactions; systemic corticosteroid at physiologic doses not to exceed 10 mg/day of prednisone or equivalent; (NOTE: If systemic corticosteroids are part of the treatment regimen for the indication under study, the systemic corticosteroid is permitted)
* Female subjects who are pregnant, breast-feeding or female patients of reproductive potential who are not employing an effective method of birth control from starting dose of durvalumab (cycle 1 day 1), including dosing interruptions through 90 days after receipt of the last dose of durvalumab are not eligible; female subjects should agree to refrain from egg cell donation while taking durvalumab and for at least 90 days after the last dose of durvalumab
* Male subjects who are not employing an effective method of birth control from starting dose of durvalumab (cycle 1 day 1), including dosing interruptions through 90 days after receipt of the last dose of durvalumab are not eligible; male subjects should agree to refrain from sperm donation while taking durvalumab and for at least 90 days after the last dose of durvalumab; should a female partner of a male patient become pregnant or suspect she is pregnant while participating in the study, he should inform his treating physician and the female partner should call her physician immediately
* History of hypersensitivity to durvalumab or any excipient
* Receipt of live attenuated vaccination within 30 days prior the first dose of durvalumab
* Patients may not be receiving any other investigational agents within 2 weeks prior to registration
* Patients who have had prior exposure to checkpoint blockade therapy, such as anti-PD-1/PD-L1, anti-cytotoxic T-lymphocyte associated protein 4 (CTLA4), anti-CD137, and anti-OX40 antibody therapy, are not eligible
* Patients who have an inter-current illness including, but not limited to any of the following, are not eligible:

  * Severe hypertension that is not controlled on medication (\>= 140/90 mmHg for 3 consecutive readings)
  * Ongoing or active infection requiring systemic treatment
  * Congestive heart failure with New York Heart Association (NYHA) classification of 3
  * Unstable angina pectoris
  * Cardiac arrhythmia
  * Psychiatric illness/social situations that would limit compliance with study requirements
  * Patients with another malignancy, unless they have been disease free for 3 years prior to registration (with the exception of squamous cell carcinoma or basal cell carcinoma of the skin or cervical intraepithelial neoplasia)
  * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints
* Unwilling or unable to comply with the protocol