This phase II trial studies how well carboplatin and nab-paclitaxel before surgery work in treating patients with triple negative breast cancer that is inflammatory or has spread from where it started to nearby tissue or lymph nodes. Drugs used in chemotherapy, such as carboplatin and nab-paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving chemotherapy before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed.

PRIMARY OBJECTIVES:

I. To test the hypothesis that carboplatin + nab-paclitaxel (paclitaxel albumin-stabilized nanoparticle formulation) therapy will demonstrate a promising neoadjuvant pathologic complete response (pCR) rate for eligible patients.

II. To test the hypothesis that carboplatin + nab-paclitaxel therapy will demonstrate a promising Symmans 0-1 pathological response rate for eligible patients.

SECONDARY OBJECTIVES:

I To evaluate the overall survival and event-free survival of eligible patients treated with carboplatin + nab-paclitaxel neoadjuvant chemotherapy.

II. To evaluate the toxicities and tolerance of carboplatin + nab-paclitaxel therapy in this patient population.

III. To evaluate the role of laboratory correlates in response, toxicity and survival endpoints.

IV. To procure tissue and perform analysis of gene and protein expression profiles of pre-treatment primary tumor (estimated success rate: 80%) and residual tumors (25%) and lymph nodes including the study of tumor niche (50%), studying sequential assessment of cellular characteristics and gene and protein expression profiles.

V. To identify specific mutations in tumor deoxyribonucleic acid (DNA) in comparison to adjacent tissue and germ line DNA procured prior to, during, and subsequent to neoadjuvant chemotherapy, and to detect/measure, as feasible, the presence of such mutations in fragmented circulating DNA from plasma, and to correlate these mutations with the presence/characteristics of circulating tumor cells in order to identify prognostic and predictive indicators of persisting/relapsed disease and targets for therapy.

VI. To assess ribonucleic acid (RNA) (using Mammaprint/Blueprint and 44,000 Agilent platform gene array), (micro) miRNA and exosome and protein profiles in tumor, adjacent tissue and plasma prior to, during, and at completion of neoadjuvant chemotherapy in order to establish prognostic and predictive indicators of outcome, markers of persistent/relapsed disease, and targets for therapy.

VII. To analyze tumor DNA and genomic DNA from plasma by microarray and reverse transcriptase (RT)-polymerase chain reaction (PCR) analysis to assess copy numbers/single nucleotide polymorphisms (SNP)/genomic polymorphisms in genes for the purposes of establishing prognostic and predictive indicators of outcomes; markers of persistence/relapse disease, drug resistance, and drug metabolism; and targets of therapy.

VIII. To assess the prognostic and predictive value of conventional pathological features (stage, estrogen and progesterone receptor and human epidermal growth factor receptor [HER-2] status, presence of lymphovascular invasion, high grade tumor status) in comparison to such values derived from the molecular approaches.

IX. To procure tumor from the primary and definitive surgical specimen for the purpose of establishing breast cancer stem cell lines.

X. To procure blood samples for the purpose of identifying and characterizing circulating tumor cells.

OUTLINE: Patients receive carboplatin intravenously (IV) over 30 minutes on day 1 and paclitaxel albumin-stabilized nanoparticle formulation IV over 30 minutes once weekly. Treatment repeats every 28 days for 4 courses in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up every 3 months for 4 years and then every 6 months for 1 year and then periodically thereafter.

Inclusion Criteria:

• Patients must be diagnosed with locally advanced (T2 and higher with or without lymph node involvement), and/or inflammatory triple negative breast cancer
• Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately
• Tumor negative for expression of hormone receptors (< 10%) and not over-expressing HER2 by immunohistochemistry (IHC) (0-1), or in case of IHC of 2, negative by fluorescence in situ hybridization (FISH) or by alternative gene testing
• Bilirubin =< 1.5 mg/dL
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2 x upper limit of normal
• Alkaline phosphatase =< 2 x upper limit of normal
• Platelets >= 100,000 cells/mm^3
• Hemoglobin > 9.0 g/dL
• Absolute neutrophil count (ANC) >= 1,500 cells/mm^3
• Creatinine =< 1.5 mg/dL is recommended; however, institutional norms are acceptable
• Left ventricular ejection fraction > 50%
• Women of childbearing potential and sexually active males must use an effective contraception method during treatment and for three months after completing treatment
• Negative serum or urine beta-human chorionic gonadotropin (hCG) pregnancy test screening for patients of childbearing potential
• All subjects must have the ability to understand and the willingness to sign a written informed consent
• No prior therapies are allowed for the treatment of the newly diagnosed breast cancer; patients with a prior diagnosis of malignancy treated >= 5 years ago are eligible, provided that they have not received prior taxanes or carboplatin as part of their prior treatment regimen, and that they meet all eligibility criteria

Exclusion Criteria:

• Known active hepatitis B or C
• Known active human immunodeficiency virus (HIV)
• Prior breast cancer or other invasive malignancy treated within 5 years
• Pregnancy
• Neuropathy > grade 1
• Any other intercurrent medical/psychological problem deemed exclusionary by the treating physician or investigators/primary investigator (PI)
• Subjects will be excluded who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study