Everolimus and Letrozole in Treating Patients With Recurrent Hormone Receptor Positive Ovarian, Fallopian Tube, or Primary Peritoneal Cavity Cancer

Inclusion Criteria: * Histologically confirmed estrogen receptor positive (greater than 10%) recurrent ovarian, fallopian tube or primary peritoneal carcinoma in post-menopausal women; note: pure clear cell and pure mucinous carcinomas are ineligible; both platinum sensitive, platinum resistant and platinum refractory disease are eligible; no limitations in the number of prior regimens * Patient has disease amenable to biopsy and is agreeable to undergo a biopsy; note: under unusual circumstances, submission of ascites material may be acceptable if a biopsy is not possible; this will require approval by one of the study principal investigators * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \> 9.0 g/dL * Total serum bilirubin =\< 2 mg/dL * Aspartate transaminase (AST) =\< 2.5 x upper limit of normal (ULN) (=\< 5 x ULN in patients with liver metastasis) * International normalized ratio (INR) =\< 2 * Creatinine =\< 1.5 x ULN * Fasting serum cholesterol =\< 300 mg/dL or =\< 7.75 mmol/L and fasting triglycerides =\< 2.5 x ULN; in case of any of these thresholds be exceeded, the patient can only be included after initiation of appropriate lipid lowering medications * Provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing to provide tissue samples for correlative research purposes Exclusion Criteria: * Any of the following * Pregnant women * Nursing women * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens including but not limited to any of the following that would limit compliance with study requirements: * Ongoing or active severe infection * Liver disease such as cirrhosis * Decompensated liver disease * Symptomatic congestive heart failure (New York heart Association class III or IV) * Unstable angina pectoris, serious uncontrolled cardiac arrhythmia, myocardial infarction =\< 6 months prior to registration * Known severely impaired lung function (spirometry and diffusing capacity of the lung for carbon monoxide \[DLCO\] 50% or less of normal and oxygen \[O2\] saturation 88% or less at rest on room air) * Active bleeding diathesis * Psychiatric illness * Known to be human immunodeficiency virus (HIV) positive * Receiving any other investigational agent =\< 4 weeks prior to registration which would be considered as treatment for the primary neoplasm * Other active malignancy =\< 3 years prior to registration; exceptions: non-melanotic skin cancer or carcinoma-in-situ of the cervix, uterus or breast; note: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer * Patients currently receiving anticancer therapies or who have received anticancer therapies =\< 4 weeks prior to registration (including chemotherapy, radiation therapy, antibody based therapy, etc.) * Known intolerance or hypersensitivity to everolimus or other rapamycin analogs (e.g. sirolimus, temsirolimus) * Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral everolimus * Uncontrolled diabetes mellitus as defined by hemoglobin (Hb)A1c \> 8% despite adequate therapy; note: patients with a known history of impaired fasting glucose or diabetes mellitus (DM) may be included, however blood glucose and antidiabetic treatment must be monitored closely throughout the trial and adjusted as necessary * Chronic treatment with corticosteroids or other immunosuppressive agents; note: topical or inhaled corticosteroids are allowed * Patients who have received live attenuated vaccines =\< 1 week prior to registration and during the study; note: patient should also avoid close contact with others who have received live attenuated vaccines; examples of live attenuated vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines * History of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study * Prior therapy with everolimus or an aromatase inhibitor * Known brain metastasis * Active and chronic viral hepatitis (i.e. quantifiable serum hepatitis B virus \[HBV\]-deoxyribonucleic acid \[DNA\] and/or positive hepatitis B virus surface antigen \[HBsAg\], or quantifiable hepatitis C virus \[HCV\]-ribonucleic acid \[RNA\] in serum)