Nab-paclitaxel and Alpelisib for the Treatment of Anthracycline Refractory Triple Negative Breast Cancer With PIK3CA or PTEN Alterations

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Stage I-III breast cancer * Confirmed invasive triple-negative breast cancer defined as estrogen receptor (ER) \< 10%; progesterone receptor (PR) \< 10% by immunohistochemistry (IHC) and HER2 negative by American Society of Clinical Oncology (ASCO)/(College of American Pathologists) CAP guidelines * Activating mutations in PIK3CA (cohort-1), or loss of function alterations in PTEN by next generation sequencing (NGS) or IHC (cohort-2) (based on MD Anderson Cancer Center \[MDACC\] Dako 6H2.1 assay) * Fasting plasma glucose (FPG) =\< 140 mg/dL (7.7 mmol/L) and glycosylated hemoglobin (HbA1c) \< 6.4 % * For patients with pre-diabetes (FPG \>= 100 mg/dL and/or HbA1c \>= 5.7%) at screening, recommend lifestyle changes according to American Diabetes Association (ADA) guidelines. A consultation with a diabetologist is highly recommended * Chemotherapy insensitive disease as defined by ARTEMIS parameters (=\< 70 % volumetric response after four cycles of anthracycline-based therapy) * Residual primary tumor size of at least 1.0 cm by imaging (ultrasound or MRI) or evidence of lymph node involvement by imaging (ultrasound or MRI) after anthracycline-based neoadjuvant chemotherapy (NACT) * Received at least one dose of an anthracycline-based NACT. Patients are eligible if therapy was discontinued due to disease progression or therapy intolerance * Prior to participation on ARTEMIS trial (2014-0185) multigated acquisition scan (MUGA) or echocardiogram showing left ventricular ejection fraction (LVEF) \>= 50% * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9 /L * Platelets \>= 100 x 10\^9 /L * Hemoglobin (Hb) \> 9 g/dL * Fasting serum amylase =\< 2 x upper limit of normal (ULN) * Fasting serum lipase =\< ULN * Total serum bilirubin =\< 1.5 mg/dL * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN or total bilirubin =\< 3.0 x ULN with direct bilirubin within normal range in patients with well documented Gilbert's syndrome * Serum creatinine =\< 1.5 x ULN or and/or creatinine clearance \> 50% lower limit of normal (LLN) * Signed informed consent obtained prior to any screening procedures * Patients must have at least 2 and no more than 5 weeks between anthracycline-based therapy and start of treatment with alpelisib and nab-paclitaxel * Patients must have resolution of toxic effect(s) of the most recent prior chemotherapy to grade 1 or less (except alopecia) * Women of childbearing potential (WCBP) must have a negative pregnancy test within 3 days prior to the first dose of study treatment. WCBP (defined as all women physiologically capable of becoming pregnant) must use highly effective methods of contraception during the study and 12 weeks after. Highly effective contraception methods include a combination of any two of the following: * Placement of an intrauterine device (IUD) or intrauterine system (IUS) * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Total abstinence * Male/ female sterilization Exclusion Criteria: * Pregnant or lactating women * Patient has a known hypersensitivity to alpelisib or any of its excipients * Patients with clinically manifest diabetes mellitus (DM) or documented steroid induced DM * Presence of distant metastatic disease (loco-regional nodal involvement of the ipsilateral axillary, internal mammary and/or supraclavicular nodes is not considered distant metastatic disease * Prior radiation therapy of the primary breast carcinoma or axillary lymph nodes * Patient is concurrently using other anti-cancer therapy * Patients with an established diagnosis of diabetes mellitus type II or uncontrolled type II based on fasting plasma glucose or HbA1c * Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study * Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of alpelisib * Male patients whose sexual partner(s) are WCBP who are not willing to use adequate contraception, during the study and for 4 weeks after the end of treatment * Patients with \> grade 1 peripheral neuropathy * Patients being treated with drugs recognized as being strong inhibitors or inducers of the isoenzyme CYP3A within the last 5 days prior to study entry * Serious concurrent illness or clinically-relevant active infection, including, but not limited to the following: * Known active hepatitis B or C * Known human immunodeficiency virus (HIV) infection * Varicella-zoster virus (shingles) * Cytomegalovirus infection * Any other known concurrent infectious disease, requiring IV antibiotics within 2 weeks of study enrollment * Clinically- significant cardiac disease: * Recent myocardial infarction (\< 6 months prior to day 1) * Unstable angina pectoris * Uncontrolled congestive heart failure (New York Heart Association \> class II) * Uncontrolled hypertension * Prior history of hypertensive crisis or hypertensive encephalopathy * Uncontrolled cardiac arrhythmias * Clinically-significant vascular disease (e.g. aortic aneurysm dissecting aneurysm) * Severe aortic stenosis * Clinically significant peripheral vascular disease * Friderica's Corrected QT interval (QTcF) \> 470 for females and \> 450 for males * History of neurological conditions that would confound assessment of treatment-emergent neuropathy * History of hemorrhagic or ischemic stroke within the last 6 months * Patient with severe liver impairment (Child Pugh score B/C) or cirrhotic liver disease * Patient has documented history of pneumonitis/interstitial lung disease * History of acute pancreatitis within 1 year of screening or past medical history of chronic pancreatitis * Patients who have a history of another primary malignancy, with the exceptions of: non-melanoma skin cancer, and carcinoma in situ of the cervix, uteri, or breast from which the patient has been disease free for 3 years * History or evidence of thrombotic or hemorrhagic disorders within 6 months before first study treatment