Selumetinib Sulfate in Treating Woman With Recurrent Low-Grade Ovarian Cancer or Peritoneum Cancer

Inclusion Criteria: * Patients age greater than 18 with the following tumors are included in the study: * Patients initially diagnosed with low-grade serous ovarian or peritoneal carcinoma that recur as low grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by Gynecologic Oncology Group \[GOG\], International Federation of Gynecology and Obstetrics \[FIGO\] World Health Organization \[WHO\] or Silverberg) * Patients initially diagnosed with serous borderline ovarian or peritoneal carcinoma that recur as low grade serous carcinoma (invasive micropapillary serous carcinoma or invasive grade I serous carcinomas as defined by GOG, FIGO WHO or Silverberg) * Patients must have measurable disease: * Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each "target" lesion must be \>= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \>= 10 mm when measured by spiral CT * Patient must have documented low grade serous carcinoma (invasive micropapillary serous); confirmation must occur before patient is considered eligible for the trial * Patients whose primary tumor was low-grade serous ovarian or peritoneal carcinoma must have a pretreatment sample of their tumor from their primary or recurrent tumor that documents low grade serous carcinoma (invasive micropapillary serous) * Patients whose primary tumor was serous borderline ovarian or peritoneal carcinoma must have a pretreatment sample of their tumor from their recurrent tumor that documents low grade serous carcinoma (invasive micropapillary serous) * Creatinine CTCAE grade 0-1 (\< 1.5 x upper limit of normal \[ULN\]) * Bilirubin CTCAE grade 0-1 (\< 1.5 x ULN) * Transaminases CTCAE grade 0-1 (\< 2.5 x ULN) * Neutrophil CTCAE grade 0-1 (\>= 1500/mcl) * Platelets CTCAE grade 0-1 (\>= 100,000/mcl) * Neuropathy =\< CTCAE grade 1 * No restrictions on prior therapy; patients cannot have previously received AZD6244 * Patients of childbearing potential must have a negative pregnancy test and must agree to practice an effective means of birth control prior to study entry, for the duration of study participation, and for four weeks after dosing with AZD6244 ceases * Patients who have met the pre-entry requirements * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients must have a GOG performance status of 0 or 1 Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive 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 AZD6244 or its excipient Captisol * Previous mitogen-activated protein kinase (MEK) inhibitor use * Patients with corrected QT (QTc) interval \> 450 msecs or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) including heart failure that meets New York Heart Association (NYHA) class III and IV definitions are excluded * Required use of a concomitant medication that can prolong the QT interval * Patients should not receive any drugs known to affect or with the potential to affect selected CYP450 isoenzymes * Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g. inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because the effects of AZD6244 on the developing human fetus at the recommended therapeutic dose are unknown; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother, breastfeeding should be discontinued if the mother is treated with AZD6244 * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with AZD6244; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated