Eribulin Mesylate in Treating Patients With Recurrent or Metastatic Salivary Gland Cancer

Inclusion Criteria: * Patients must have histologically or cytologically documented salivary gland cancers; patients that do not have a salivary gland primary must have one of the following histologies - adenoid cystic carcinoma, mucoepidermoid carcinoma, acinic cell carcinoma * Patients must have recurrent and/or metastatic disease that is progressive and not amenable to surgery or curative radiotherapy occurring within 6 months of study entry, as evidenced by: at least a 20% increase in radiographically or clinically measurable disease, appearance of any new lesions, or deterioration in clinical status * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Patients with measurable disease per RECIST 1.1 criteria * At least one lesion of \>= 1.5 cm in long-axis diameter for non lymph nodes or \>= 1.5 cm in short-axis diameter for lymph nodes which is serially measurable according to RECIST 1.1 using either computerized tomography (CT) or magnetic resonance imaging (MRI) * Lesions that have had radiotherapy must show evidence of progressive disease (PD) based on RECIST 1.1 to be deemed a target lesion * Absolute neutrophil count \>= 1,500/μL * Platelets \>= 100,000/μL * Creatinine clearance \>= 40 mL/min * Bilirubin =\< 1.5 upper limit of normal (ULN) * Alkaline phosphatase =\< 3 ULN; if total ALP is \> 3 x ULN (in the absence of liver metastasis) or \> 5 x ULN in subjects with liver metastasis AND the subject is known to have bone metastases, th…