Talazoparib and HSP90 Inhibitor AT13387 in Treating Patients With Metastatic Advanced Solid Tumor or Recurrent Ovarian, Fallopian Tube, Primary Peritoneal, or Triple Negative Breast Cancer

Inclusion Criteria:

* For the dose escalation cohort, patients must have histologically or cytologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective
* For the dose expansion cohort, participants must have histologically or cytologically confirmed diagnosis of either: i) ovarian, fallopian tube, or primary peritoneal cancer of high grade serous histology which has recurred despite standard therapy or ii) triple-negative breast cancer which has recurred despite standard therapy
* There is no line limit for the dose escalation cohort and the dose expansion cohort
* For the dose expansion cohort, patients with ovarian, fallopian tube or primary peritoneal cancer must have platinum resistant disease defined as progression within 6 months after last platinum regimen; platinum refractory disease is allowed
* For the dose expansion cohort, patients with triple-negative breast cancer may not be breast cancer 1/2 (BRCA1/2) germline mutation carriers
* There must be availability of a formalin-fixed, paraffin-embedded tumor specimen with adequate viable tumor tissue
* Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60)
* Life expectancy of greater than 12 weeks
* Leukocytes \>= 3,000/mcL
* Hemoglobin \>= 9 g/dL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin within normal institutional limits
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) = \< 2.5 × institutional upper limit of normal
* Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Left ventricular ejection fraction \> 50% on echocardiography or multigated acquisition (ECHO/MUGA) scan
* Corrected QT (QTc) =\< 450 ms
* Any clinically significant electrolyte imbalance, particularly hypokalemia and hypomagnesemia, should be corrected before treatment
* Have undergone clearance after baseline ophthalmologic exam (at least fundoscopic exam, visual acuity, intraocular pressure, assessment of visual fields and measurement of color vision)
* For the expansion cohort only: measurable disease by RECIST v1.1 with at least one measurable target lesion
* 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 and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of BMN 673 and/or AT13387 administration
* Patients must be able to swallow pills and have no significant impairment in gastrointestinal absorption
* Three biopsies, one pretreatment, one after BMN673 alone and one after one of the combinations of BMN673/AT13387 will be voluntary in the expansion and dose escalation cohorts; however, biopsies will be required in at least 8 patients of the 20 patients to be enrolled in the expansion cohort
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
* All acute, clinically significant treatment-related toxicity from prior therapy, except for alopecia, must have resolved to grade =\< 1
* Patients who are receiving any other investigational agents
* Patients with known brain metastases should be excluded from this clinical trial
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to BMN 673 and AT13387 used in study
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with BMN 673 or AT13387
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
* Known history of QT/QTc prolongation or torsades de pointes (TdP); patients who are currently receiving treatment with medication with a known risk to prolong the QT interval or inducing torsades de pointes and the treatment cannot either be discontinued or switched to a different medication prior to starting study drugs