Local Consolidative Therapy and Durvalumab for Oligoprogressive and Polyprogressive Stage III NSCLC After Chemoradiation and Anti-PD-L1 Therapy

Inclusion Criteria: * Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol * Stage III NSCLC (AJCC 7th and 8th edition) patients who received standard chemoradiation followed by durvalumab therapy with either progressive disease or persistent disease. Persistent disease defined as residual positron emission tomography (PET) avidity 6 months after completion of initial definitive therapy and confirmed with biopsy * For lung adenocarcinoma patients, patients must not harbor any EGFR sensitizing mutations, ALK fusion, ROS1 rearrangements, RET fusions, or MET exon 14 skipping mutations where there are standard of care therapy options available. For patients with histologies other than adenocarcinoma, EGFR and ALK status is not required. Adenocarcinoma patients may be consented prior to the EGFR, ALK, and ROS1 status being known, but EGFR, ALK, and ROS1 status must be determined prior to initiating therapy. EGFR, ALK, and ROS ALK status may be determined using either tumor- or plasma-based, Clinical Laboratory Improvement Act (CLIA)-certified assays. For patients with NSCLC, not otherwise specified (NOS), EGFR testing is not required, as the frequency of alterations is exceedingly rare in this histology * Cohort A: Oligoprogressive disease is defined as having 3 or fewer lesions of progression (sites can be local, distant, or both). Multiple mediastinal lesions will be counted as 1 lesion * Cohort B: Polyprogressive disease defined as having greater than 3 lesions of progression (sites can be local, distant, or both). Multiple mediastinal lesions will be counted as 1 lesion * Candidate for radiation therapy to at least one lesion * Tumor assessment by computed tomography (CT) scan with contrast chest/abdomen/pelvis or PET-CT, and magnetic resonance imaging (MRI) brain must be performed within 28 days prior to study entry * Age \>= 18 years at time of study entry * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Body weight \> 30 kg * Hemoglobin \>= 9.0 g/dL * Platelet count \>= 75 × 10\^9/L * Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be =\< 5 x ULN * Measured creatinine clearance (CL) \> 15 mL/min or calculated creatinine CL \> 15 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance * Patient 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 * Must have a life expectancy of at least 12 weeks Exclusion Criteria: * Patients who rapidly progressed on the PACIFIC regimen (chemoradiotherapy \[CRT\] + durvalumab). This is defined as any progression on the first 3-month imaging scan after starting durvalumab post-CRT * Patients who were treated with anti-PD-(L)1 therapy other than durvalumab * Participation in another clinical study with an investigational product during the last 4 weeks * Concurrent enrolment in another clinical study, unless it is an observational (non-interventional) clinical study. No other investigational therapy is permitted after durvalumab and start of this protocol * Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies) =\< 28 days prior to the first dose of study drug. This 28 day washout period is not required for durvalumab. If sufficient wash-out time has not occurred due to the schedule or pharmacokinetic (PK) properties of an agent, a longer wash-out period will be required, as agreed by AstraZeneca and the investigator * 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 * Any concurrent chemotherapy (with the exception of protocol directed chemotherapy in the polyprogression cohort), investigational product (IP), biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable * Major surgical procedure (as defined by the investigator) within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent is acceptable * History of allogenic organ transplantation * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome) 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 * 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 adverse events (AEs) or compromise the ability of the patient to give written informed consent * History of another primary malignancy except for * Malignancy treated with curative intent and with no known active disease \>= 3 years before the first dose of IP and of low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease * History of leptomeningeal carcinomatosis * Patients with suspected brain metastases at screening should have an MRI (preferred) or CT each preferably with IV contrast of the brain prior to study entry. Brain metastases must be treated prior to enrolment and demonstrate radiographic stability (defined as 2 brain images, both of which are obtained after treatment to the brain metastases. These imaging scans should both be obtained at least four weeks apart and show no evidence of intracranial progression). Treated brain metastases will be counted as lesions treated as part of the protocol. In addition, any neurologic symptoms that developed either as a result of the brain metastases or their treatment must have resolved or be stable either, without the use of steroids, or are stable on a steroid dose of =\< 10mg/day of prednisone or its equivalent and anticonvulsants for at least 14 days prior to the start of treatment * Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) \>= 470 ms calculated from 3 electrocardiograms (ECGs) (within 15 minutes at 5 minutes apart) * History of active primary immunodeficiency * 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 (known positive hepatitis B virus \[HBV\] surface antigen (HBsAg) result), hepatitis C patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA) * Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab. 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., CT scan premedication) * Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 30 days after the last dose of IP * Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab monotherapy * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients * Patients who have received prior anti-PD-1, anti PD-L1 or anti CTLA-4: * Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy * All AEs while receiving prior immunotherapy must have completely resolved or resolved to baseline prior to screening for this study * Must not have experienced a \>= grade 3 immune related AE or an immune related neurologic or ocular AE of any grade while receiving prior immunotherapy. NOTE: Patients with endocrine AE of =\< grade 2 are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic * Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not currently require maintenance doses of \> 10 mg prednisone or equivalent per day * Judgment by the investigator that the patient is unsuitable to participate in the study and the patient is unlikely to comply with study procedures, restrictions and requirements