Pemetrexed Disodium/Observation in Treating Patients W/ Malignant Pleural Mesothelioma w/Out Progressive Disease After 1st Line Chemotherapy

Inclusion Criteria: * Histologically confirmed malignant pleural mesothelioma meeting 1 of the following cell types: * Epithelial * Sarcomatoid * Mixed type * Histologically documented malignant pleural mesothelioma, epithelial, sarcomatoid or mixed type, not amenable to surgical resection * Prior treatment * Currently receiving first-line treatment with pemetrexed + platinum; patients are to be registered to Cancer and Leukemia Group B (CALGB) 30901 no later than the last day of cycle 4 of first line therapy * Prior intracavitary cytotoxic or sclerosing therapy (including bleomycin) are acceptable; prior intrapleural cytotoxic chemotherapy will not be considered systemic chemotherapy * Prior surgical treatment is allowed * Prior radiation therapy is allowed * Non-pregnant and non-nursing; women of child bearing potential and men must agree to use an appropriate method of birth control throughout their participation in this study; appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives (Norplant), or double barrier methods (diaphragm plus condom) * RANDOMIZATION ELIGIBILITY CRITERIA * Patients with complete response, partial response, or stable disease following 4, 5 or 6 cycles of first-line chemotherapy with pemetrexed AND either cisplatin or carboplatin; a maximum of 6 cycles of chemotherapy may have been given * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Granulocytes \>= 1,500/ul * Platelet count \>= 100,000/ul * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2 x ULN * Calculated creatinine clearance \>= 45 ml/min * Disease not amenable to surgery * Must be enrolled on imaging protocol CALGB-580903 * Complete response, partial response, or stable disease after completion of 4 courses of first-line chemotherapy comprising pemetrexed disodium AND cisplatin or carboplatin * Study therapy will begin within 9 weeks following day 1 of cycle 4 of first-line treatment * No clinically significant pleural or peritoneal effusions that cannot be adequately managed by drainage before or during pemetrexed disodium PATIENT CHARACTERISTICS: * ECOG performance status of 0-1 * Life expectancy ≥ 12 weeks * Granulocytes ≥ 1,500/μL * Platelet count ≥ 100,000/μL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST ≤ 2 times ULN * Creatinine clearance ≥ 45 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No psychiatric illness that would prevent the patient from giving informed consent * No second malignancy except non-melanoma skin cancer or carcinoma in situ of the cervix unless curatively treated with no evidence of active disease for ≥ 5 years * No medical conditions that, in the opinion of the treating physician, would make study treatment unreasonably hazardous for the patient including, but not limited to, the following: * Ongoing or active infection such as HIV positivity * Inability to take oral medications * Psychiatric illness/social situations that would limit compliance with study requirements PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Prior intracavitary cytotoxic or sclerosing therapy (including bleomycin) allowed * Prior intrapleural cytotoxic chemotherapy not considered systemic chemotherapy * Prior surgery allowed * Prior radiotherapy allowed * No concurrent palliative radiotherapy * No concurrent hormones or other chemotherapeutic agents except for the following: * Steroids for adrenal failure * Hormones for nondisease-related conditions (e.g., insulin for diabetes) * Intermittent use of dexamethasone as an antiemetic or premedication for pemetrexed disodium