Inclusion Criteria:
* All subjects must have the ability to understand and the willingness to sign a written informed consent
* Ability to undergo standard PET imaging
* Plan to be treated with immunotherapy
* Karnofsky performance status (KPS) \>= 50%
* Absolute neutrophil count (ANC) \>= 1000/mm\^3
* Platelet count \>= 50/mm\^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment
* Total bilirubin =\< 1.5 x the upper limit of normal (ULN)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN
* Calculated creatinine clearance \>= 30 mL/min
* Woman of childbearing potential must be practicing a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies: e.g., established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device or intrauterine system; barrier methods; condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization; true abstinence (when this is in line with the preferred and usual lifestyle of the subject) during and after the study (6 months after the last dose of 64Cu-anti-PD1 \[pembrolizumab\]-N-hydroxysuccinimide \[NHS\]-DOTA for women)
* A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control, e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 6 months after receiving the last dose of study drug
Exclusion Criteria:
* Prior exposure to pembrolizumab or other anti-PD1 therapy
* Unable to tolerate PET scan
* Any condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Female patients who are lactating or have a positive pregnancy test during the screening period
* Infection requiring systemic antibiotic therapy within 14 days prior to start of study treatment
* Subject is receiving concurrent chemotherapy or biologic or hormonal therapy for cancer treatment. Subject is receiving bone marrow stimulatory factors (e.g., granulocyte-macrophage colony-stimulating factor \[GM-CSF\]). Note: Concurrent use of hormones for noncancer-related conditions (e.g., insulin for diabetes) is acceptable
* Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study
* Vaccination with live attenuated vaccines within 4 weeks of study agent administration
* Subject is currently using or has used immunosuppressive medication within 14 days prior to the study agent administration
* Intranasal, topical, inhaled, or local steroid injections (e.g., intra-articular injection)
* Chronic systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent
* Steroids as premedication for hypersensitivity reactions (e.g., infusion-related reactions, computed tomography \[CT\] scan premedication)
* Subject has plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), or primary amyloidosis
* Subject has known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% predicted normal. Note that FEV1 testing is required for patients suspected of having COPD and subjects must be excluded if FEV1 \< 50%
* Subject has known allergies, hypersensitivity, or intolerance to monoclonal antibodies or human proteins, or their excipients
* Subject has history of primary immunodeficiency
* Subject is positive for human immunodeficiency virus (HIV-1), chronic or active hepatitis B, or active hepatitis A or C
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)