Talazoparib and Low-Dose Temozolomide in Treating Participants With Relapsed or Refractory Extensive-Stage Small Cell Lung Cancer

Inclusion Criteria: * Able to provide informed consent. * Cytologically or histologically confirmed small cell lung cancer (SCLC) with extensive-stage disease. * Relapsed (progressed within 6 months) or refractory (progressed during or within 4 weeks of completing 1st line platinum based regimen). * Measurable disease, as per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Archival or fresh tissue biopsy available for exploratory analyses. * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1. * Able to swallow the study drugs, has no known intolerance to study drugs or excipients, and able to comply with study requirements. * Female participants of childbearing potential must have a negative pregnancy test at screening and must agree to use a highly effective birth control method (defined in protocol) from the time of the first study drug treatment through 45 days after the last study drug treatment. * Male participants must use a condom when having sex from the time of the first study drug treatment through 105 days after the last study drug treatment. Contraception should be considered for a non-pregnant female partner of childbearing potential. * Male and female participants must agree not to donate sperm or eggs, respectively, from the first study drug treatment through 105 days and 45 days after the last study drug treatment, respectively. * Female participants may not be breastfeeding at baseline through 45 days after the last study drug treatment. * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Glomerular filtration rate (by Cockroft-Gault or equivalent estimation) \>= 30 mL/min * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for participants with liver metastases * Serum total bilirubin =\< 1.5 X upper limit or normal (ULN) OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 ULN * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless participant is receiving anticoagulant therapy, as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants Exclusion Criteria: * Has not recovered (recovery is defined as Common Terminology Criteria for Adverse Events (CTCAE) version (v)4 grade =\< 1 or return to baseline) from the acute toxicities of previous therapy, except treatment-related alopecia or laboratory abnormalities otherwise meeting eligibility requirements. * Best response of progressive disease per RECIST 1.1 to first-line platinum doublet chemotherapy. * Has received more than 1 line of cytotoxic therapy * Prior immunotherapy and targeted therapies (including rovalpituzumab tesirine) are allowed. * Prior treatment with a PARP inhibitor (not including iniparib) or temozolomide. * Use of antineoplastic therapies within 14 days before study treatment initiation. * Use of any other investigational agent within 14 days before study treatment initiation. * Received radiation therapy within 14 day before study treatment initiation (single fraction palliative radiotherapy is allowed without a washout). * Prior thoracic irradiation and prophylactic cranial irradiation are allowed. * Major surgery within 14 days before study treatment initiation. * Diagnosis of myelodysplastic syndrome (MDS). * Gastrointestinal disorder affecting absorption. * Current or anticipated use of a prohibited P-gp inhibitor or P-gp inducer or BCRP inhibitors. * History of another cancer within 2 years before study treatment initiation, with the exception of fully treated cancers unlikely to affect the assessment of the study treatment safety or efficacy including early stage breast, prostate, nonmelanomatous skin, thyroid, cervix and endometrial cancer. * Any condition (concurrent disease, infection, or comorbidity) that interferes with ability to participate in the study, causes undue risk, or complicates the interpretation of safety data, in the opinion of the investigator.