Pegylated Irinotecan NKTR 102 in Treating Patients With Relapsed Small Cell Lung Cancer

Inclusion Criteria: * Written informed consent granted prior to initiation of any study-specific screening procedures, given with the understanding that the patient has the right to withdraw from the study at any time, without prejudice * Histologic or cytologic diagnosis of SCLC (Note: patients with mixed histology are not eligible) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Presence of measurable disease defined as \>= 1 lesion whose longest diameter can be accurately measured as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) * Previously treated SCLC with only one prior treatment regimen (cyclophosphamide/doxorubicin/vincristine \[CAV\] alternating with etoposide/cisplatin \[EP\] is acceptable) * Resolution of all acute toxic effects of prior chemotherapy, radiotherapy, hormonal therapy, or surgery to National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 grade =\< 1, except for diarrhea (which must be grade 0 without supportive antidiarrheal medications) and alopecia (any grade) * Platelet count \>= 100 x 10\^9/L * Hemoglobin (Hgb) \>= 9 gm/dL * Absolute neutrophil count (ANC) \>= 1500/uL * Serum creatinine =\< 1.5 mg/dL or creatinine clearance \> 45 mL/min; use either measured or calculated with Cockcroft-Gault formula * Serum total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN or =\< 5 x ULN if caused by liver metastasis * Women of childbearing potential must have a negative pregnancy test performed within seven days prior to the start of study drug; male and female subjects of child-bearing potential must agree to use double-barrier contraceptive measures, or avoidance of intercourse during the study and for 6 months after last investigational drug dose received Exclusion Criteria: * Previous anti-cancer chemotherapy, immunotherapy or investigational agents \< 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to the first day of study defined treatment; palliative radiation \< 2 weeks, biological therapy within 2 weeks, hormonal therapy within 1 week prior to day 1 cycle 1 * Prior treatment with a topoisomerase-I inhibitor (e.g., topotecan, irinotecan) * Prior malignancy except for non-melanoma skin cancer and carcinoma in situ, unless diagnosed and definitively treated more than 5 years prior to enrollment * Substance abuse, medical, psychological or social conditions that may, in the opinion of the Investigator, interfere with the patient's participation in the study or evaluation of the study results * Known human immunodeficiency virus (HIV) infection * Pregnancy or breast-feeding * Concurrent administration or received cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers or inhibitors within 2 weeks prior to the first day of study drug treatment * Patients with chronic or acute gastrointestinal (GI) disorders resulting in diarrhea of any severity grade; patients who are using chronic anti-diarrheal supportive care (more than 3 days/week) to control diarrhea in the 28 days prior to study entry * Major surgery \< 4 weeks or minor surgery (e.g. talc pleurodesis, excisional biopsy, etc) \< 2 weeks prior to the first day of study defined treatment * Have central nervous system (CNS) metastases (unless the patient has completed successful local therapy for CNS metastases and has been off corticosteroids for at least 4 weeks before starting study therapy); brain imaging is required in symptomatic patients to rule out brain metastases, but is not required in asymptomatic patients * 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 * Unwilling or unable to follow protocol requirements