Temsirolimus and Bevacizumab in Treating Patients With Advanced Endometrial, Ovarian, Liver, Carcinoid, or Islet Cell Cancer

Inclusion Criteria: * Histologically or cytologically confirmed endometrial (endometrioid, uterine, papillary serous carcinoma, and carcinosarcoma), ovarian (primary peritoneal/fallopian tube, serous, endometrioid, mixed, and poorly differentiated epithelial ovarian cancers \[for purposes of eligibility, carcinosarcoma is considered a poorly differentiated carcinoma\]), hepatocellular carcinoma, carcinoid or islet cell (neuroendocrine: well- or moderately-differentiated neuroendocrine) cancer which are locally advanced, recurrent, or metastatic * Patients must have measurable disease; patients having only lesions measuring \>= 1 cm to \< 2 cm must use spiral computed tomography (CT) imaging for both pre- and post-treatment tumor assessments; patients who have had prior palliative radiotherapy to metastatic lesion(s) must have at least one measurable lesion(s) that have not been previously irradiated * Radiation therapy (adjuvant or palliative) must be completed \>= 4 weeks prior to registration, if applicable * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets \>= 75,000/mm\^3 * Hemoglobin \>= 9.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN); Note: direct bilirubin and international normalized ratio (INR) for hepatocellular carcinoma (HCC) patients allowed as per Child-Turcotte-Pugh scoring * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN if liver metastasis is present or patient is in HCC cohort) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 x ULN (=\< 5 x ULN if liver metastasis is present or patient is in HCC cohort) * Creatinine =\<1.5 x ULN * Urinalysis \< 2+ protein; urine protein should be screened by dipstick or urine analysis; for proteinuria \>= 2+, 24-hour urine protein should be obtained and the level should be \< 2 g for patient enrollment * Fasting serum cholesterol =\< 350 mg/dL (=\< 9.0 mmol/L) * Triglycerides =\< 1.5 x ULN (mg/dL or mmol/L); patients with triglyceride levels \> 1.5 x ULN can be started on lipid lowering agents and reevaluated within 1 week; if levels go to =\< 1.5 x ULN, they can be considered for the trial and continue the lipid lowering agents; NOTE: cholesterol and triglyceride measurement and management are not required for single-agent bevacizumab cohort with islet cell carcinoma * International normalized ratio (INR) =\< 1.5 (unless the patient is on full dose warfarin) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1 * Capable of understanding the investigational nature, potential risks and benefits of the study and able to provide valid informed consent * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only; NOTE: patients and their partners should be practicing an effective form of contraception during the study and for at least 3 months following the last dose of this combined therapy * Full-dose anticoagulants, if a patient is receiving full-dose anticoagulants (except carcinoid tumors), the following criteria should be met for enrollment: the subject must have an in-range INR (usually between 2 and 3) on a stable dose of warfarin or on stable dose of low molecular weight (LMW) heparin * Prior systemic treatments for metastatic disease are permitted, including targeted therapies, biologic response modifiers, chemotherapy, hormonal therapy, or investigational therapy; exception: in the case of endometrial cancer no prior chemotherapy for metastatic or recurrent disease is allowed; prior planned adjuvant chemotherapy is allowed * Patients who have had prior anthracycline must have a normal ejection fraction on left ventricular ejection fraction (LVEF) assessment by multigated acquisition scan (MUGA) or echocardiogram (Echo) =\< 4 weeks prior to registration * Availability of tissue if applicable (from the primary tumor or metastases) for tumor studies for banking; Note: in the case of hepatocellular cancer if diagnosed by clinical and radiologic criteria only, availability of tissue not applicable * Willingness to donate blood for biomarker studies related to the type of therapies used in this trial and the tumor types being treated * ENDOMETRIAL CANCER (PERMANENTLY CLOSED TO ENROLLMENT) * Any hormonal therapy directed at the malignant tumor is allowed; NOTE: therapy must be discontinued at least one week prior to registration * Prior systemic therapy including biologic and immunologic agents as adjuvant treatment, must be discontinued at least 3 weeks prior to registration * Recurrent or persistent endometrial adenocarcinoma, uterine papillary serous carcinoma and carcinosarcoma which is refractory to curative therapy or established treatments; NOTE: histologic or cytologic confirmation of original primary tumor is required * HEPATOCELLULAR CANCER (PERMANENTLY CLOSED TO ENROLLMENT) * HCC confirmed by biopsy OR diagnosed by clinical and radiologic criteria; all of the following criteria must be met or a biopsy is required: * Known cirrhosis or chronic hepatitis B virus (HBV) or hepatitis C virus (HCV) infection * Hypervascular liver masses \> 2 cm, and either serum alpha-fetoprotein (AFP) \> 400 ng/ml, or * AFP \> three times normal and doubling in value in the antecedent 3 months * Child-Pugh A (=\< 6 points) or better liver status * Prior regional treatments for liver metastasis are permitted including: * Selective internal radiation therapy such as brachytherapy, cyberknife, radiolabeled microsphere embolization, etc. * Hepatic artery chemoembolization * Hepatic artery embolization * Hepatic artery infusional chemotherapy * Radiofrequency ablation NOTE: patients must be \>= 4 weeks from treatment and show progressive disease in the liver after regional therapy or must have measurable disease outside the liver * Concomitant anti-viral therapy is allowed * History of prior varices or evidence of varices on pre-study CT/magnetic resonance imaging (MRI) imaging are required to undergo endoscopy =\< 4 weeks prior to registration; those who had received specific therapy (banding and/or sclerotherapy) and had not bled within the prior 6 months are eligible * Suitably recovered from prior localized therapy, in the opinion of the investigator * ISLET CELL CANCER AND CARCINOID TUMOR (PERMANENTLY CLOSED TO ENROLLMENT) * Patient has evidence of progressive disease as documented by Response Evaluation Criteria in Solid Tumors (RECIST) =\< 7 months prior to study entry * Carcinoid tumor cohort: prior and concurrent long-acting somatostatin analogue therapy is required; patient has to be on a stable dose of a long-acting somatostatin analogue \>= 2 months prior to study entry with documentation of progressive disease on current dose * Islet cell tumor cohort: prior and/or concurrent long-acting somatostatin analogue therapy is allowed, but not required; if patient is continued on a long-acting somatostatin analogue, a stable dose for \>= 2 months prior to study entry is required with documentation of progressive disease on current dose * Prior therapies allowed include: * =\< 2 prior chemotherapy regimens * Prior interferon \>= 4 weeks prior to registration * Radiolabeled octreotide therapy (patients with prior radiolabeled octreotide therapy should have progressive disease after such therapy) * Other investigational therapy NOTE: islet Cell Single Agent Bevacizumab Cohort: Prior mammalian target of rapamycin (mTOR) inhibitor is allowed * Prior regional treatments for liver metastasis are permitted including: * Selective internal radiation therapy such as brachytherapy, cyberknife, radiolabeled microsphere embolization, etc. * Hepatic artery chemoembolization * Hepatic artery embolization * Hepatic artery infusional chemotherapy * Radiofrequency ablation NOTE: patients must be \>= 12 weeks from treatment and show progressive disease in the liver after regional therapy or must have measurable disease outside the liver Exclusion Criteria: * Prior therapy with vascular endothelial growth factor receptor (VEGFR) targeting agents or mammalian target of rapamycin (mTOR) inhibitors (except as in HCC and in the Islet cell single agent bevacizumab alone cohort where prior mTOR inhibitor is allowed); Note: prior use of bevacizumab is not allowed in any cohort * Invasive procedures defined as follows: * Major surgical procedure, open biopsy or significant traumatic injury =\< 4 weeks prior to registration * Anticipation of need for major surgical procedures during the course of the study * Core biopsy =\< 7 days prior to registration * Serious or non-healing wound, ulcer or bone fracture * History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess =\< 180 days prior to first date of bevacizumab therapy * Evidence of bleeding diathesis or coagulopathy in the absence of therapeutic anticoagulation * Evidence of a history bleeding =\< 6 months such as hemoptysis, or cerebrovascular accident =\< previous 6 months, or peripheral vascular disease with claudication on \< 1 block, or history of clinically significant bleeding, because of the potential bleeding and/or clotting risk with bevacizumab * Untreated central nervous system (CNS) metastases; exceptions: patients with known CNS metastases can be enrolled if the brain metastases have been adequately treated and there is no evidence of progression or hemorrhage after treatment as ascertained by clinical examination and brain imaging (MRI or CT) =\< 12 weeks prior to registration and no ongoing requirement for steroids * Anticonvulsants (stable dose) are allowed * Patients who had surgical resection of CNS metastases or brain biopsy =\< 3 months prior to registration will be excluded * Significant cardiovascular disease defined as congestive heart failure (New York Heart Association class II, III or IV), angina pectoris requiring nitrate therapy, or recent myocardial infarction (=\< 6 months prior to registration) * Uncontrolled hypertension (defined as a blood pressure of \>= 150 mmHg systolic and/or \>= 90 mmHg diastolic) * Patient is on angiotensin-converting-enzyme (ACE) inhibitors (benazapril, captopril, enalopril, fosonopril, lisinopril, moexipril, perindopril, quinopril, ramipril, and trandolapril); (patients may have an alternate antihypertensive substituted); NOTE: ACE inhibitors are allowed in single agent bevacizumab cohort * Currently active, second malignancy other than non-melanoma skin cancers; NOTE: patients are not considered to have a 'currently active' malignancy if they have completed anti-cancer therapy and are considered by their physician to be at less than 30% risk of relapse * Any of the following, as this regimen may be harmful to a developing fetus or nursing child: * Pregnant women * Breastfeeding women * Men or women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception (diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) NOTE: the effects of the agent(s) on the developing human fetus at the recommended therapeutic dose are unknown * Known hypersensitivity to other recombinant human antibodies or Chinese hamster ovary cell products * Other uncontrolled serious medical or psychiatric condition (e.g. cardiac arrhythmias, diabetes, etc.) * Current therapy with a cytochrome P450 3A4 (CYP3A4) inhibitor or inducer; NOTE: these agents are allowed in the single-agent bevacizumab islet cell carcinoma cohort * Active infection requiring antibiotics * Active bleeding or pathological conditions that carry high risk of bleeding (e.g. tumor involving major vessels, known varices) * Known human immunodeficiency virus (HIV)-positive * ENDOMETRIAL CANCER (PERAMANENTLY CLOSED TO ENROLLMENT) * Received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of endometrial cancer * Any chemotherapy for metastatic or recurrent cancer * Radiation therapy to \> 25% of marrow bearing areas * HEPATOCELLULAR CANCER EXCLUSION (PERMANENTLY CLOSED TO ENROLLMENT) * Child-Pugh B or C classification * Grade \>= 3 hemorrhage =\< 4 weeks prior to registration * Prior liver transplant with evidence of recurrent or metastatic disease * Patients on an active liver transplant list and considered likely to receive a liver transplant =\< 6 months following registration * Clinical evidence of encephalopathy * Prior treatment with sorafenib or other vascular endothelial growth factor (VEGF) inhibitors; NOTE: Exceptions allowed for patients unable to tolerate the agent; intolerance is defined in this protocol as a discontinued agent due to side effects with an exposure \< to 4 weeks of drug, at any dose level * OVARIAN CANCER (PERMANENTLY CLOSED TO ENROLLMENT) * Clinical signs and symptoms of gastrointestinal (GI) obstruction and require parental hydration/nutrition or tube feeding * Evidence of free abdominal air not explained by paracentesis or recent surgical procedures * Received more than two prior cytotoxic chemotherapy regimens for persistent or recurrent disease * CARCINOID (PERMANENTLY CLOSED TO ENROLLMENT) * Patients on anticoagulant therapy