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 …