Nab-Paclitaxel and Bevacizumab in Treating Patients With Unresectable Stage IV Melanoma or Gynecological Cancers

Inclusion Criteria: * Age \>= 18 years * Melanoma cohort only: histologic proof of surgically unresectable stage IV malignant melanoma * Melanoma cohort only: measurable disease defined as at least one lesion whose longest diameter can be accurately measured as \>= 2.0 cm with chest x-ray, or as \>= 1.0 cm with computed tomography (CT) scan or magnetic resonance imaging (MRI) scan; or CT component of a positron emission tomography (PET)/CT; NOTE: disease that is measurable by physical examination only is not eligible * Gynecologic cancer cohorts only (dose escalation and dose expansion cohorts) * Dose escalation cohort only: Histologic proof of epithelial cervical, endometrial, ovarian, fallopian, or primary peritoneal cancers; allowable histologies for cervical cancer include squamous cell carcinoma, adenocarcinoma, and mixed/adenosquamous carcinoma; allowable histologies for endometrial cancer include endometrioid, serous, clear cell, mucinous, squamous, transitional cell, undifferentiated, mixed, and carcinosarcoma (this is considered a poorly differentiated epithelial tumor); allowable histologies for ovarian, fallopian, and peritoneal cancer include serous, clear cell, endometrioid, mucinous, transitional cell, undifferentiated, mixed, and carcinosarcoma * Endometrial cancer expansion cohort only: * Histologic proof of endometrial cancer including endometrioid, serous, clear cell, mucinous, undifferentiated, mixed, and carcinosarcoma histologies * 1-3 lines of c…