Atezolizumab With Chemotherapy in Treating Patients With Anaplastic or Poorly Differentiated Thyroid Cancer (NCT03181100)

Usually NOT eligible if any of the following apply:

• Exclusion Criteria:
• Subjects with an active, known or suspected autoimmune disease. Subjects with type I diabetes mellitus on stable insulin regimen, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll.
• For patients not receiving therapeutic anticoagulation: INR or partial thromboplastin time (aPTT) \> 1.5 x ULN within 28 days prior to initiation of study treatment.
• Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway targeting agents. Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose, and no history of severe immune-related adverse effects from anti-CTLA 4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] grade 3 and 4).
• Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease.
• History of human immunodeficiency virus (HIV) infection or active hepatitis B (chronic or acute) or hepatitis C infection Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible. However, patients with past or resolved hepatitis B virus (HBV) should be monitored for reactivation by a specialist. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA).
• Pregnant or lactating women. All pre-menopausal women being screened must have a negative serum pregnancy test within 14 days prior to commencement of dosing. Women of non-childbearing potential may be included if they are either surgically sterile or have been postmenopausal for \>= 1 year. Fertile men and women must use an effective method of contraception during treatment and for at least 6 months after completion of treatment as directed by their physician.
• Untreated brain metastases.
• Chemotherapy within 21 days of enrollment with the exception of paclitaxel or nab-paclitaxel (Abraxane). Patients who have received one course of these agents prior to study entry are eligible. (One course of weekly paclitaxel or nab-paclitaxel is 3 doses. One course of every 3 week dosing of paclitaxel or nab-paclitaxel is 1 dose). Patients who have received prior radiosensitizing chemotherapy are eligible.
• The use of corticosteroids is not allowed for 10 days prior to initiation of atezolizumab except patients who are taking steroids for physiological replacement. Inhaled or topical steroids, and adrenal replacement steroid doses are permitted in the absence of active autoimmune disease. This does not apply to patients receiving steroids as pre-medications for paclitaxel administration.
• Grade \>= 2 uncontrolled hypertension (patients with a history of hypertension controlled with anti-hypertensive medication to Grade =\< 1 are eligible).
• ADDITIONAL EXCLUSION CRITERIA FOR non-BRAF/non-RAS MUTATION (COHORT 3):