The main purpose of this study is to see whether the combination of selinexor (KPT-330) can help people with triple negative breast cancer (TNBC). Researchers also want to study the safety and tolerability of Selinexor in TNBC patients.

Inclusion Criteria:

• Histologically confirmed triple negative breast cancer (TNBC), defined as negative immunohistochemical staining for estrogen and progesterone receptors (≤5% of nuclei positive by IHC) and receptor tyrosine-protein kinase erbB-2 (HER2) negative (IHC 0-1+ or HER2-neu negative according to American Society of Clinical Oncology; College of American Pathologists (ASCO-CAP) HER2 Test Guideline Recommendations)
• Written informed consent in accordance with federal, local, and institutional guidelines
• Body surface area ≥1.4 m^2
• Age ≥18 years
• Estimated life expectancy of >3 months at study entry
• TNBC must be either locally recurrent or metastatic. Locally recurrent disease must not be amenable to surgical resection or radiation with curative intent.
• Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1
• Documented disease progression at study entry
• Must have received at least 1 chemotherapy regimens in the setting of metastatic disease
• Eastern Cooperative Oncology Group (ECOG) performance status of ≤2
• Adequate hematological function: Absolute neutrophil count (ANC) > 1500/mm^3, platelets count >100,000mm^3
• Adequate hepatic function within 14 days prior to Cycle 1 Day 1 (C1D1): total bilirubin <2 times the upper limit of normal (ULN) (except patients with Gilbert's syndrome who must have a total bilirubin of < 3 times ULN) and aspartate aminotransferase (AST), alanine aminotransferase (ALT) ≤2.5 x ULN. In the case of known (radiological and/or biopsy documented) liver metastasis, AST/ALT ≤5.0 times ULN is acceptable.
• Amylase and lipase ≤ 1.5 x ULN
• Adequate renal function within 14 days prior to C1D1: estimated creatinine clearance of ≥ 30 mL/min
• Women of child-bearing potential (WOCBP) must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male participants must use an effective barrier method of contraception if sexually active with a female of child-bearing potential. For both male and female participants, effective methods of contraception must be used throughout the study and for 3 months following the last dose. To be considered of non-childbearing potential, postmenopausal women must be amenorrheic for at least 12 months naturally (not in the setting of post chemotherapy) or participants must be surgically sterile.
• Must have received prior anthracycline and taxane therapy unless clinically contraindicated

Exclusion Criteria:

• Significant medical illness that in the investigator's opinion cannot be adequately controlled with appropriate therapy or would compromise the participant's ability to tolerate this therapy
• Women who are pregnant or lactating
• Radiation, chemotherapy, or immunotherapy or any other approved anticancer therapy ≤2 weeks prior to cycle 1 day 1
• Major surgery within 4 weeks before Day 1
• Unstable cardiovascular function: Electrocardiogram (ECG) abnormalities requiring treatment, or congestive heart failure (CHF) of New York Hearth Association (NYHA) Class ≥3; myocardial infarction (MI) within 3 months
• Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose. Potential participants with controlled infection or on prophylactic antibiotics are permitted in the study.
• Known history of HIV
• Known active hepatitis A, B, or C infection that requires treatment
• Any underlying condition that would significantly interfere with the absorption of an oral medication
• Grade >2 peripheral neuropathy at baseline (within 14 days prior to cycle 1 day 1)
• Participation in an investigational anti-cancer study within 3 weeks prior to Cycle 1 Day 1
• Coagulation problems and active major bleeding within 4 weeks prior to C1D1 (peptic ulcer, epistaxis, spontaneous bleeding)
• Active central nervous system (CNS) malignancy. Asymptomatic small lesions are not considered active. Treated lesions may be considered inactive if they are stable for at least 3 months.
• Radiation, chemotherapy, or immunotherapy or any other anticancer therapy ≤ 2 weeks prior to Cycle 1 Day 1 or radio-immunotherapy ≤ 4 weeks prior to Cycle 1 Day 1
• Have not recovered to Grade ≤ 1 or to their baseline from clinically significant adverse effects

All participants

10 months