Selumetinib With or Without Temsirolimus in Treating Patients With Metastatic, Recurrent, or Locally Advanced Soft Tissue Sarcoma That Cannot Be Removed By Surgery

Inclusion Criteria:

* Patients must have had histologic verification of soft-tissue sarcoma at original diagnosis (GIST subtype is eligible)
* Patients must have metastatic (de novo or recurrent) or locally advanced, unresectable disease; patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan
* ECOG 0-2 (Karnofsky \>= 50%)
* Patients may have received 0-2 prior cytotoxic chemotherapeutic regimens for metastatic or recurrent disease (single-agent or combination chemotherapies)
* Estimated life expectancy \> 12 weeks
* Peripheral absolute neutrophil count (ANC) \>= 1000/uL
* Platelet count \>= 100,000/uL (transfusion independent)
* Hemoglobin \>= 8.0 gm/dL (may receive RBC transfusions)
* Creatinine =\< 1.5 x upper institutional limits of normal, or calculated creatinine clearance \>= 45mL/min, based on the Cockcroft-Gault formula
* Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age
* SGPT (ALT) =\< 5 x upper limit of normal (ULN) for age
* No evidence of dyspnea at rest, no exercise intolerance
* Pulse oximetry \> 94% if there is clinical indication for determination
* For women: must be surgically sterile, postmenopausal, or compliant with a medically approved contraceptive regimen (for example, intrauterine device \[IUD\], birth control pills, or barrier device) during and until 4 weeks after the last dose of study treatment; must have a negative serum or urine pregnancy test within 7 days before study enrollment, and must not be breast-feeding; should a woman become pregnant or suspect she is pregnant while she or her partner participating in this study, the patient should inform her treating physician immediately; for men: must be surgically sterile or compliant with a contraceptive regimen during and for 16 weeks after the treatment period; please note that the AZD6244 manufacturer recommends that adequate contraception for male patients should be used for 16 weeks post-last dose due to sperm life cycle
* All patients must sign a written informed consent

Exclusion Criteria:

* Patients with pediatric-type sarcomas (Ewing's or primitive neuroectodermal tumor, rhabdomyosarcoma, and desmoplastic small round cell tumor)
* Concomitant Medications

  * Growth factor(s): growth factors that support platelet or white cell number or function must not have been administered within the past 7 days
  * Steroids: patients with CNS tumors who have not been on a stable or decreasing dose of dexamethasone for the past 7 days
  * Investigational Drugs: patients who are currently receiving another investigational drug
  * Anti-cancer Agents: patients who are currently receiving other anti-cancer agents; at least 3 weeks must have elapsed since prior chemotherapy or radiation (6 weeks for mitomycin-C and nitrosureas)
* 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
* Previous MEK inhibitor use
* Patients with 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); this may be determined by either Bazett's correction (QTc =QT/RR0.5) or Friderica's correction (QTc = QT/RR0.33); QTc exclusion \> 450 msec requires calculation according to both formulas
* Patients unable to swallow the AZD6244 capsules are ineligible
* 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, uncontrolled, 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
* 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
* Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study
* Prior cardiac history of uncontrolled hypertension, New York Heart Association (NYHA) Classification \>= class II, current or prior cardiomyopathy, baseline LVEF \< 50%, ongoing atrial fibrillation, recent myocardial infarction or unstable ischemic heart disease
* Concomitant Strong CYP1A2 or CYP3A4 inducers and/or inhibitors; prior treatment with an mTOR inhibitor for recurrent soft-tissue sarcoma