Carboplatin and Paclitaxel With or Without Atezolizumab Before Surgery in Treating Patients With Newly Diagnosed, Stage II-III Triple-Negative Breast Cancer

Inclusion Criteria: * Patients must have histologically confirmed new diagnosis of breast cancer * Estrogen receptor (ER) and progesterone receptor (PR) \< Allred score of 3 or =\< 5% positive staining cells in the invasive component of the tumor (provided the patient is being treated as triple negative breast cancer) * Human epidermal growth factor receptor 2 (HER2) negative by fluorescence in situ hybridization (FISH) or immunohistochemistry (IHC) staining 0 or 1+ according to National Comprehensive Cancer Network (NCCN) guidelines * Clinical stage T2-T4c, any N, M0 primary tumor by American Joint Committee on Cancer (AJCC) 7th edition clinical staging * Eligible for neoadjuvant chemotherapy * No prior therapy for this disease * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 150,000/mcL * Hemoglobin \>= 10 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Creatinine clearance \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault * International normalized ratio (INR) =\< 1.5 x ULN (this applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose) * Activated partial thromboplastin time (aPPT) =\< 1.5 x ULN (this applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose) * Administration of atezolizumab may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 180 days after the last dose of paclitaxel; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign an Institutional Review Board (IRB) approved written informed consent document Exclusion Criteria: * Known metastatic disease * Invasive cancer in the contralateral breast * Patients with a previous history of non-breast malignancy are eligible only if they meet the following criteria for a cancer survivor: (1), and (2) * Has undergone potentially curative therapy for all prior malignancies * Has been considered disease-free for at least 1 year (with the exception of basal cell or squamous cell carcinoma of the skin or carcinoma-in-situ of the cervix) * Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation * Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1 * Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1 * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., osteoporosis) is allowed * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * History of allergic reactions attributed to compounds of similar chemical or biologic composition to other agents used in study * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease * Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible * Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations * Rash must cover less than 10% of body surface area (BSA) * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%) * No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted * Patients with active tuberculosis (TB) are excluded * Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1 * Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible * Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study with the exception of the planned breast cancer surgery that is part of the trial design * Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab * Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study * Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia (including symptomatic sinus bradycardia), or psychiatric illness/social situations that would limit compliance with study requirements * Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have: * A stable regimen of highly active anti-retroviral therapy (HAART) * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections * A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests * Pregnant women are excluded from this study because atezolizumab is an agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezolizumab, breastfeeding should be discontinued if the mother is treated with atezolizumab; these potential risks may also apply to other agents used in this study