Sorafenib in Treating Patients With Extensive Stage Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically-confirmed diagnosis of small cell lung cancer and must have extensive disease with progression or recurrence after receiving a standard first-time regimen containing either cisplatin or carboplatin; patients who receive primary curative chemoradiation therapy for limited disease, but who recur within the primary tumor site, previously radiated field or with distant metastases are also allowed to participate; diagnosis based on sputum cytology is acceptable if confirmation by an independent pathologic review at the institution is documented; patients who have clinical evidence of recurrent small cell lung cancer do not require a confirmatory biopsy to be eligible for this trial * Patients must have measurable disease per RECIST criteria; patients must have evidence of disease by plain radiographs, CT scan or MRI scan; all x-rays/scans to assess measurable disease must have been performed within 28 days prior to registration; all other required test to assess non-measurable disease must be performed within 42 days prior to registration; all disease must be assessed * Patients must have been previously treated with exactly one regimen; this must have included cisplatin or carboplatin; in addition, information must be available to place the patient in one of the two following categories: * Platinum sensitive disease: defined as an initial response to platinum-based chemotherapy who subsequently progressed \> 90 days after last platinum treatment; best response to platinum-based treatment: CR, PR, stable or progression while on treatment (circle one); NOTE: Prior chemotherapy must have been completed at least 90 days prior to registration OR * Platinum refractory disease; no response to platinum-based chemotherapy, progression during platinum-based therapy, or progression within 90 days of completing platinum-based therapy * Patient may have receive previous radiation therapy, but it must have been completed at least 21 days prior to registration and the patient should have recovered from all associated toxicities; there must be no plans for the patients to receive concurrent radiation therapy to measurable lesions; measurable disease may be present inside the area of prior radiation therapy provided that the lesion is demonstrated to be progressing by CT scan or there is measurable disease outside the prior radiation field * Patients may have received prior surgery provided that at least 14 days have elapsed since surgery (thoracic or other major surgeries) and the patient has recovered from all associated toxicities; patients must have disease outside the area of previous surgical resection or a new lesion must be present * CORRELATIVE SCIENCE STUDIES: Institutions must have IRB approval of S9925 (the Lung Cancer Specimen Repository); patients must be offered participation in S9925; with the patient's consent, specimens will be submitted for testing via S9925; patients must be registered separately to S9925 in order for institutions to receive credit for specimen submission * Serum creatinine =\< the institutional upper limit of normal OR creatinine clearance \>= 60 cc/min * Bilirubin =\< 2 x the institutional upper limit of normal * Alkaline phosphatase =\< 2 x the institutional upper limit of normal * SGOT or SGPT =\< 2 x the institutional upper limit of normal * PTT and either PT or INR \< 1.5 x the institutional upper limit of normal (except in patients who are on warfarin \[Coumadin or heparin\] obtained within 28 days prior to registration); patients who receive anti-coagulation treatment with an agent such as warfarin or heparin, prophylactically or therapeutically, will be allowed to participate * Patients must not have any evidence of bleeding diathesis * ANC \>= 1,500/uL * Platelet count \>= 100,000/uL * Patients must have a Zubrod performance status 0-1 * Patients with known brain and/or leptomeningeal metastases are eligible only if he/she is asymptomatic, without deficits on neurologic exam and is not receiving corticosteroid therapy to control symptoms; only a non-enzyme inducing anticonvulsant (e.g., Keppra) will be permitted for those patients requiring anticonvulsants; all patients must have a pretreatment CT or MRI scan of the brain to evaluate CNS disease within 28 days prior to registration * Any ongoing requirement for systemic corticosteroid therapy is not permitted; topical and/or inhaled steroids are allowed * Patients must either be able to swallow and/or receive enteral medications via gastrostomy feeding tube; patients with intractable nausea or vomiting are not eligible; patients with GI tract disease resulting in an inability to take oral medication, malabsorption syndrome, a requirement for IV alimentation, prior surgical procedures affecting absorption, or uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis) are not eligible * The effects of BAY 43-9006 on the developing human fetus at the recommended therapeutic dose are unknown; for this reason, patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method (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 participating in this study, she should inform her treating physician immediately * Patients must not have a significant history of cardiac disease, e.g., uncontrolled hypertension, unstable angina, congestive-heart failure, and myocardial infarction within the last six months, or cardiac ventricular arrhythmias requiring medication * Patients must be willing to provide prior smoking history * No other prior malignancy is allowed 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 5 years * All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * At the time of patient registration, the treating institution's name and ID number must be provided to the Data Operations Center in Seattle in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the data base