A Phase I Trial of Combination Gemcitabine and Nab-Sirolimus in Advanced Leiomyosarcomas or Advanced Soft-Tissue Sarcomas With TSC2 or TSC1 Loss-of-function Mutations or Deletions

Inclusion Criteria: 1. Patients must have histologically confirmed leiomyosarcoma or sarcoma with TSC2 or TSC1 loss-of-function mutations or deletions based on standard-of-care genomic testing. 2. Sarcoma that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective. One prior standard systemic therapy is required for leiomyosarcoma (LMS) Patients. 3. Prior gemcitabine-based chemotherapy is allowed if the last dose of gemcitabine was given more than 12 months prior to the first dose of treatment on trial, there was no progression of disease while on treatment with gemcitabine, and there was intolerable toxicity. 4. 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 for non-nodal lesions and short axis for nodal lesions) as ≥20 mm (≥2 cm) by chest x-ray or as ≥10 mm (≥1 cm) with CT scan, MRI, or calipers by clinical exam. 5. Age ≥18 years. Because no dosing or adverse event data are currently available on the use of nab-sirolimus in combination with gemcitabine in patients \<18 years of age, children are excluded from this study. 6. ECOG performance status ≤2 (Karnofsky ≥60%,). 7. Life expectancy of \>3 months, as determined by the investigator. 8. Patients must have adequate organ and marrow function as defined below: i. absolute neutrophil count ≥1,500/mcL ii. platelets ≥100,000/mcL iii. hemoglobin ≥9 gm/dL iv. total bilirubin ≤ 2 x institutional upper limit of normal (ULN) (except patients with Gilbert's syndrome, who must have total bilirubin \< 3.0 mg/dL) v. AST(SGOT)/ALT(SGPT) ≤2 × institutional ULN vi. eGFR (calculated by CKD-EPI) ≥ 60 mL/min vii. Serum triglyceride \<300 mg/dL viii. Serum cholesterol \<350 mg/dL 9. For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. 10. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For Participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. 11. Patients with Human Immunodeficiency Virus (HIV) with a viral load \<400copies/mL, no IADS-defining illness within 12 months of enrollment, and no CYP3A4 inducers or inhibitors in the antiretroviral treatment. 12. Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression. 13. Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better. 14. The effects of nab-sirolimus on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from the time of study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). Negative serum HCG will be required before study drug administration. This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: Postmenopausal (no menses in greater than or equal to 12 consecutive months). History of hysterectomy or bilateral salpingo-oophorectomy. Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range). History of bilateral tubal ligation or another surgical sterilization procedure. Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Patient/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 15. Ability to understand and the willingness to sign a written informed consent document. Exclusion: 1. Patients who are receiving any other investigational agents or have received any other investigational agent within 3 weeks prior to enrollment. 2. History of allergic reactions attributed to compounds of similar chemical or biologic composition to nab-sirolimus or gemcitabine. 3. Use of strong inhibitors and inducers of CYP3A4 within the 7 days prior to receiving the first dose of nab-sirolimus. Additionally, use of any known CYP3A4 substrates with narrow therapeutic window (such as fentanyl, alfentanil, astemizole,cisapride, dihydroergotamine, pimozide, quinidine, terfanide) within the 7 days prior to receiving the first dose of nab-sirolimus. 4. Patients with active concurrent malignancy. 5. Recent stroke or thromboembolic event (within 6 months) requiring anticoagulation that cannot be interrupted. Non-life threatening deep venous thrombosis on stable anticoagulation within 6 months is allowed. 6. Active gastro-intestinal bleeding. 7. Pre-existing thyroid abnormality is allowed provided thyroid can be controlled with medication. 8. Prior treatment with radiotherapy (including radio-labeled spheres and/or cyberknife, hepatic arterial embolization (with or without chemotherapy) or cyrotherapy/ablation) is allowed if these therapies did not affect the areas of measurable disease being used for this protocol. 9. Uncontrolled diabetes mellitus as defined by HbA1c \>8% despite adequate therapy. 10. Evidence of severe or uncontrolled systemic disease or any other concurrent condition, including psychiatric, that would significantly limit the ability to participate safely in this study. 11. Pregnant women are excluded from this study because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nab-sirolimus, breastfeeding should be discontinued if the mother is treated with nab-sirolimus. These potential risks may also apply to other agents used in this study. 12. Prior treatment of sarcoma with mTOR inhibitors. 13. Vulnerable populations will not be enrolled.