Inclusion Criteria:

* Patients must meet all SCREENING/PRE-SCREENING and SUB-STUDY REGISTRATION COMMON ELIGIBILITY CRITERIA as specified in S1400: Phase II/III Biomarker-Driven Master Protocol for Previously Treated Squamous Cell Lung Cancer (Lung-Map)
* Patients must be assigned to S1400G; S1400G biomarker eligibility defined as homologous recombination repair deficiency (HRRD) positive is as follows

* Biomarker-positive group

* HRRD by FMI

* Homologous recombination repair deficiency by Foundation Medicine Inc., criteria
* Alteration type

* Truncating mutation, frameshift deletions, indels missense and nonsense mutations predicted to have functional consequence in any of the specified genes
* Eligible alteration

* Mutation in any one of the following critical HRR pathway genes: ATM, ATR, BARD1, BRCA1, BRCA2, BRIP1, CHEK1, CHEK2, FANCA, FANCC, FANCD2, FANCF, FANCM, NBN (NBS1), PALB2, RAD51, RAD51B (RAD51L1), RAD54L, RPA1
* Patients must not have had prior exposure to any agent with a PARP inhibitor (e.g., veliparib, olaparib, rucaparib, niraparib, talazoparib \[BMN 673\]) as its primary pharmacology
* Patients must have achieved stable disease, a partial response, or a complete response at their first disease assessment after initiating first-line platinum-based chemotherapy; patients determined to have progressed (in the opinion of the treating physician) at their first disease assessment are not eligible
* Patients may not have any impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of talazoparib (BMN 673) (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small bowel resection, or active peptic ulcer disease); patients must not have active small or large intestine inflammation such as Crohn's disease or ulcerative colitis (within 12 months of sub-study registration)
* Patients must be able to take oral medications; patients must be able to swallow capsules whole without crushing or altering them in any way
* Patients must not be taking, nor plan to take while on protocol treatment strong P-glycoprotein (P-gp) inhibitors, P-gp inducers, or breast cancer resistance protein (BCRP) inhibitors; the language ?P-gp or BCRP inhibitors or inducers? is reworded to ?strong P-gp inhibitors, P-gp inducers, or BCRP inhibitors? for consistency with the investigator brochure
* Patients must agree to have blood specimens submitted for pharmacokinetic analysis