LN-145 or LN-145-S1 in Treating Patients With Relapsed or Refractory Ovarian Cancer, Triple Negative Breast Cancer (TNBC), Anaplastic Thyroid Cancer, Osteosarcoma, or Other Bone and Soft Tissue Sarcomas

Inclusion Criteria: * Age between 18 and 70 (Subjects aged 16-70 may be enrolled into the osteosarcoma cohort). * Subjects must be willing and able to provide informed consent. For patients \< 18 years of age, their parents or legal guardians must sign a written informed consent. Assent, when appropriate, will be obtained according to institutional guidelines. * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 or 1. * Subjects must have an area of tumor amenable to excisional biopsy (core biopsies may be allowed as detailed in protocol) for the generation of TIL separate from, and in addition to, a target lesion to be used for response assessment. * Any prior therapy directed at the malignant tumor, including radiation therapy, chemotherapy, and biologic/targeted agents must be discontinued at least 28 days prior to enrollment for preparing TIL therapy. Palliative therapy may be received during the screening period with principal investigator (PI) approval for lesions that are not expected to be used for TIL generation or as target lesions. * Absolute neutrophil count (ANC) \>= 1000/mm\^3 (within 7 days of enrollment). * Hemoglobin \>= 8.0 g/dL (transfusion allowed) (within 7 days of enrollment). * Platelet count \>= 100,000/mm\^3 (within 7 days of enrollment). * Alanine aminotransferase (ALT)/serum glutamate pyruvate transaminase (SGPT) and aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) =\< 2.5 x the upper limit of …