Linsitinib or Topotecan Hydrochloride in Treating Patients With Relapsed Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed SCLC * Patients must have measurable disease; at least one lesion that can be accurately measured is required * Patients must have progression of disease after receiving ONLY 1 previous platinum-containing regimen; prior treatment with biological response modifiers or targeted agents will NOT count towards this requirement; previous topotecan or any type of pharmacologic IGF-1R inhibition are NOT allowed * Life expectancy of greater than 6 weeks * Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 2; (Karnofsky \>= 60%) * Leukocytes (white blood cell \[WBC\]) \>= 3,000/mcL OR * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits (NIL) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 times institutional upper limit of normal (ULN) without demonstrable liver metastases OR \< 5.0 times ULN with liver metastases present * Serum creatinine within NIL OR measured/calculated creatinine clearance (CrCl) \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above NIL * Fasting blood glucose \< 160 mg/dL at baseline * Patients on oral antihyperglycemic therapies may be enrolled provided they have been taking a stable dose of these medications for \>= 2 weeks at the time of randomization * Prior radiation is permitted IF the site(s) of measurable disease has progressed since prior irradiation and radiation is completed at least 2 weeks before initiation of drug treatment (stereotactic radiotherapy excluded) * Patients with central nervous system (CNS) metastases are ELIGIBLE, provided that prior to drug treatment, the metastases have been treated, remain clinically or radiographically stable and the patient has no significant neurologic symptoms * Patients must NOT have prior malignancy EXCEPT for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease-free for \>= 3 years * Women of child-bearing potential (WOCBP) 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; WOCBP must provide a negative pregnancy test (serum or urine) within 14 days prior to registration * Available archival tumor tissue is NOT mandatory for enrollment (will be requested) * Patients must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * Patients with CNS metastases are NOT EXCLUDED, provided that prior to drug treatment, the metastases have been treated, remain radiographically stable and the patient has no significant neurologic symptoms * History of allergic reactions attributed to compounds of similar chemical or biologic composition to OSI-906 or other agents used in the study (topotecan) * While cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2) inhibitors/inducers are not specifically excluded, investigators should be aware that the metabolism and consequently overall pharmacokinetics (PKs) of OSI-906 (OSI-906 exposure) could be altered by concomitant use of these drugs (inhibitors, inducers and/or other substrates of CYP1A2); exception: potent CYP1A2 inhibitors ciprofloxacin and fluvoxamine are prohibited; while cytochrome P450, family 2, subfamily C, polypeptide 9 (CYP2C9) substrates are not specifically excluded, investigators should be aware that levels of drugs metabolized by CYP2C9 may be increased by the concomitant administration of OSI-906; caution should be used when administering CYP2C9 substrates to study patients * The concomitant use of p-glycoprotein inhibitors with topotecan capsules is not allowed * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, significant cardiac disease (i.e., symptomatic congestive heart failure, unstable angina pectoris, symptomatic or life-threatening cardiac arrhythmia), or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or breast-feeding women are excluded from this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients in the following scenarios are excluded: * Corrected QT (QTc) interval \> 450 msec at baseline * Concomitant drugs that prolong the QTc interval * Use of drugs that have a known risk of causing Torsades de Pointes (TdP) within 14 days prior to randomization * Fasting blood glucose \>= 160 mg/dL at baseline; these patients can initiate allowed oral antihyperglycemic therapies and be retested or rescreened 2 weeks later to meet baseline fasting blood glucose criteria * Concomitant use of insulin or insulinotropic medications * Patients with cirrhosis of the liver are excluded from this study * Archival tumor tissue is NOT mandatory for enrollment, but will be requested