Gemcitabine With or Without Pazopanib in Treating Patients With Refractory Soft Tissue Sarcoma

Inclusion Criteria: * Subjects must provide written informed consent prior to performance of study-specific procedures or assessments, and must be willing to comply with treatment and follow-up; procedures conducted as part of the subject's routine clinical management (e.g., blood count, imaging study) and obtained prior to signing of informed consent may be utilized for screening or baseline purposes provided these procedures are conducted as specified in the protocol * Histologically confirmed diagnosis of metastatic or unresectable soft tissue sarcoma, excluding gastrointestinal stromal tumors, Kaposi's sarcoma, Ewing's family of tumors, and embryonal or alveolar rhabdomyosarcoma * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Patients must have received at least one, but not more than three, systemic regimens for treatment of metastatic soft tissue sarcoma; patients must have had a prior anthracycline in the neoadjuvant, adjuvant, or metastatic setting unless medically inappropriate for the patient * Neoadjuvant or adjuvant therapy will not count towards prior treatment for metastatic disease, unless the patient relapsed within 2 years of completing such therapy. * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Hemoglobin \>= 8 g/dL; subjects may not have had a transfusion within 7 days of screening assessment * Platelets \>= 100 x 10\^9/L * Prothrombin time (PT) or international normalized ratio (INR) =\< 1.2 x upper limit of normal (ULN); subjects receiving anticoagulation therapy are eligible if their INR is stable and within the recommended range for the desired level of anticoagulation * Activated partial thromboplastin time (aPTT) =\< 1.2 x ULN * Total bilirubin =\< 1.5 x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN; concomitant elevations in bilirubin and AST/ALT above 1.0 x ULN (upper limit of normal) are not permitted * Serum creatinine =\< 1.5 mg/dL (133 umol/L) * Or, if \> 1.5 mg/dL: calculated creatinine clearance (ClCR) \>= 30 mL/min * Urine protein to creatinine ratio (UPC) \< 1; if UPC \>= 1, then a 24-hour urine protein must be assessed; subjects must have a 24-hour urine protein value \< 1 g to be eligible; use of urine dipstick for renal function assessment is not acceptable * Or 24-hour urine protein \< 1 g * A female is eligible to enter and participate in this study if she is of: * Non-childbearing potential (i.e., physiologically incapable of becoming pregnant), including any female who has had: * A hysterectomy * A bilateral oophorectomy (ovariectomy) * A bilateral tubal ligation * Is post-menopausal * Subjects not using hormone replacement therapy (HRT) must have experienced total cessation of menses for \>= 1 year and be greater than 45 years in age, OR, in questionable cases, have a follicle stimulating hormone (FSH) value \> 40 mIU/mL and an estradiol value \< 40 pg/mL (\< 140 pmol/L) * Subjects using HRT must have experienced total cessation of menses for \>= 1 year and be greater than 45 years of age OR have had documented evidence of menopause based on FSH and estradiol concentrations prior to initiation of HRT * Childbearing potential, including any female who has had a negative serum pregnancy test within 7 days prior to the first dose of study treatment, preferably as close to the first dose as possible, and agrees to use adequate contraception; defined as follows: * Complete abstinence from sexual intercourse for 14 days before exposure to investigational product, through the dosing period, and for at least 21 days after the last dose of investigational product * Oral contraceptive, either combined or progesterone alone * Injectable progesterone * Implants of levonorgestrel * Estrogenic vaginal ring * Percutaneous contraceptive patches * Intrauterine device (IUD) or intrauterine system (IUS) with a documented failure rate of less than 1% per year * Male partner sterilization (vasectomy with documentation of azoospermia) prior to the female subject's entry into the study, and this male is the sole partner for that subject * Double barrier method: condom and an occlusive cap (diaphragm or cervical/vault caps) with a vaginal spermicidal agent (foam/gel/film/cream/suppository) * Female subjects who are lactating should discontinue nursing prior to the first dose of study drug and should refrain from nursing throughout the treatment period and for 14 days following the last dose of study drug Exclusion Criteria: * Prior malignancy; note: subjects who have had another malignancy and have been disease-free for \> 3 years, or subjects with a history of completely resected non-melanomatous skin carcinoma, successfully treated in situ carcinoma, or successfully treated superficial bladder cancer are eligible. * History or clinical evidence of central nervous system (CNS) metastases or leptomeningeal carcinomatosis, except for individuals who have previously-treated CNS metastases, are asymptomatic, and have had no requirement for steroids or anti-seizure medication for 6 months prior to first dose of study drug; screening with CNS imaging studies (computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) is required only if clinically indicated or if the subject has a history of CNS metastases * Clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding including, but not limited to: * Active peptic ulcer disease * Known intraluminal metastatic lesion/s with risk of bleeding * Inflammatory bowel disease (e.g. ulcerative colitis, Crohn's disease), or other gastrointestinal conditions with increased risk of perforation * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days prior to beginning study treatment * Clinically significant gastrointestinal abnormalities that may affect absorption of investigational product including, but not limited to: * Malabsorption syndrome * Major resection of the stomach or small bowel * Presence of uncontrolled infection * Corrected QT interval (QTc) \> 480 msecs using Bazett's formula * History of any one or more of the following cardiovascular conditions within the past 6 months: * Cardiac angioplasty or stenting * Myocardial infarction * Unstable angina * Coronary artery bypass graft surgery * Symptomatic peripheral vascular disease * Class III or IV congestive heart failure, as defined by the New York Heart Association (NYHA) * Poorly controlled hypertension (defined as systolic blood pressure \[SBP\] of \>= 140 mmHg or diastolic blood pressure \[DBP\] of \>= 90mmHg); note: initiation or adjustment of antihypertensive medication(s) is permitted prior to study entry; following antihypertensive medication initiation or adjustment, blood pressure (BP) must be re-assessed three times at approximately 2-minute intervals; at least 24 hours must have elapsed between anti-hypertensive medication initiation or adjustment and BP measurement; these three values should be averaged to obtain the mean diastolic blood pressure and the mean systolic blood pressure; the mean SBP/DBP ratio must be \< 140/90 mmHg * History of cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or untreated deep venous thrombosis (DVT) within the past 6 months; note: subjects with recent DVT who have been treated with therapeutic anti-coagulating agents for at least 6 weeks are eligible * Prior major surgery or trauma within 28 days prior to first dose of study drug and/or presence of any non-healing wound, fracture, or ulcer (procedures such as catheter placement not considered to be major) * Evidence of active bleeding or bleeding diathesis * Known endobronchial lesions and/or lesions infiltrating major pulmonary vessels that increase the risk of pulmonary hemorrhage * Hemoptysis in excess of 2.5 mL (or one half teaspoon) within 8 weeks of first dose of study drug * Any serious and/or unstable pre-existing medical, psychiatric, or other condition that could interfere with subject's safety, provision of informed consent, or compliance to study procedures * Unable or unwilling to discontinue use of prohibited medications for at least 14 days or five half-lives of a drug (whichever is longer) prior to the first dose of study drug and for the duration of the study; administration of any non-oncologic investigational drug within 30 days or 5 half-lives whichever is longer prior to receiving the first dose of study treatment * Treatment with any of the following anti-cancer therapies: * Radiation therapy, surgery or tumor embolization within 14 days prior to the first dose of pazopanib OR * Chemotherapy, immunotherapy, biologic therapy, investigational therapy or hormonal therapy within 14 days (or 28 days in the case of monoclonal antibody therapy) prior to the first dose of pazopanib. * Any prior treatment with pazopanib. * Prior treatment with vascular endothelial growth factor (VEGF) or vascular endothelial growth factor receptor (VEGFR)-targeting agents other than pazopanib (eg. sorafenib, sunitinib, and bevacizumab) in the metastatic setting. Prior use of such agents in the neoadjuvant or adjuvant setting is permitted. * Any prior treatment with gemcitabine for metastatic disease. Prior use of gemcitabine in the neoadjuvant or adjuvant setting is permitted. * Any ongoing toxicity from prior anti-cancer therapy that is \> grade 1 and/or that is progressing in severity, except alopecia