Topotecan Hydrochloride or Cyclodextrin-Based Polymer-Camptothecin CRLX101 in Treating Patients With Recurrent Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed small cell lung cancer * All patients must have extensive stage disease; extensive stage patients are defined as those patients with bilateral or contralateral supraclavicular adenopathy or contralateral hilar adenopathy or malignant pleural effusion or extrathoracic metastatic disease * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Patients must have been treated with 1 prior platinum-based (cisplatin or carboplatin) regimen; prior thoracic radiation for limited stage disease is allowed; patients must be at least 4 weeks since prior chemotherapy or radiation * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * 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 x 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 * Baseline imaging studies performed =\< 28 days of study registration * The effects of CRLX101 on the developing human fetus are unknown; 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 CRLX101 administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 2 weeks to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who have previously been treated with irinotecan or topotecan * Patients who are receiving any other investigational agents * Patients with uncontrolled brain metastases; patients with treated brain metastases must have stable neurologic status off of steroids and anticonvulsants for at least 2 weeks and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CRLX101 or topotecan * Patients with 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 * Previous or concurrent malignancy; exceptions: treated basal cell or squamous cell skin cancer, in situ cervical cancer, or lobular carcinoma in situ in one breast; or other cancer which the patient has been disease-free \>= 5 years * Pregnant women and women who are capable of reproduction but who will not agree to use adequate contraception prior to study entry and for the duration of study participation; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with CRLX101 or topotecan, breastfeeding should be discontinued if the mother is treated with either agent * Human immunodeficiency virus (HIV)-positive patients * Patients with history of inflammatory bowel disease requiring therapy or patients with chronic diarrhea syndromes or paralytic ileus