Radiotherapy in Combination With Atezolizumab in Locally Advanced Borderline Resectable or Unresectable Cutaneous SCC

Inclusion Criteria: * Histologically or cytologically confirmed locally advanced borderline resectable or unresectable cSCC and oligometastatic (1-3 sites of metastatic disease) cSCC receiving therapy to the primary * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 10 mm with computed tomography (CT) scan or \> 10 mm with calipers by clinical exam by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Written informed consent and any locally-required authorization (e.g., Health Insurance Portability and Accountability Act \[HIPAA\] in the United States of America \[USA\], European Union \[EU\] Data Privacy Directive in the EU) obtained from the patient prior to performing any protocol-related procedures, including screening evaluations * Age \>= 18 years at time of study entry * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Life expectancy \>= 24 weeks * Body weight \> 30 kg * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L (\>= 1000 per mm\^3) * Platelet count \>= 75 x 10\^9/L (\>= 75,000 per mm\^3) * 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 * Serum albumin 25 g/L (2.5 g/dL) * Measured creatinine clearance (CL) \> 40 mL/min or calculated creatinine CL\>40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance * For patients receiving therapeutic anticoagulation: stable anticoagulant regimen * 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) * 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 Exclusion Criteria: * Participation in another clinical study with an investigational product during the last 3 months * Patients with active interstitial lung disease (ILD)/pneumonitis or with a history of ILD/pneumonitis requiring steroids * Concurrent enrolment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study * Any previous treatment with a PD1 or PD-L1 inhibitor, including atezolizumab, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 \[IL-2\]) within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment * Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies, other investigational agent) 30 days prior to the first dose of study drug for patients who have received prior tyrosine kinase inhibitors (TKIs) \[e.g., erlotinib, gefitinib and crizotinib\] and within 6 weeks for nitrosourea or mitomycin C. (If sufficient wash-out time has not occurred due to the schedule or pharmacokinetics (PK) properties of an agent, a longer wash-out period may be required.) * Patients with corrected QT (QTc) interval \> 470 msec during screening * Current or prior use of immunosuppressive medication within 14 days (use 28 days if combining atezolizumab with a novel agent) before the first dose of atezolizumab, 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., CT scan premedication) * Any concurrent chemotherapy, investigational product (IP), biologic, or hormonal therapy that is not part of standard National Comprehensive Cancer Network (NCCN) indicated head and neck squamous cell carcinoma (HNSCC) adjuvant concurrent chemoradiotherapy (CRT). Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable * History of allogenic organ or bone marrow 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, idiopathic pulmonary fibrosis, organizing pneumonia, uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently), uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium ULN), uncontrolled tumor-related pain, 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 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, or human immunodeficiency virus (positive human immunodeficiency virus \[HIV\] 1/2 antibodies). 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 virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA * 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 atezolizumab and up to 5 months after the last dose of atezolizumab * Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ highly effective birth control from screening to 5 months after the last dose of atezolizumab monotherapy. Patient must have a negative serum pregnancy test within 72 hours of study entry * Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation * History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins * Prior randomization or treatment in a previous atezolizumab clinical study * 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