Comparing the New Anti-cancer Drug Eribulin With Chemotherapy Against the Usual Chemotherapy Alone in Metastatic Urothelial Cancer

Inclusion Criteria: * Participant must have predominant histologically or cytologically proven urothelial carcinoma in a metastatic site * Participant must have evidence of metastatic urothelial carcinoma based on CT or MRI within 28 days prior to registration * Participant must have had progression of disease following prior therapy at the discretion of the treating investigator * Participants must not require immediate central nervous system (CNS)-specific treatment, in the opinion of the treating investigator if they have active brain metastases (defined as new or progressive brain metastases) or leptomeningeal disease * Participant must have had prior systemic therapy in metastatic setting that: * Included enfortumab vedotin * Included a PD1/PDL1 antibody * NOTE: Under the discretion of the treating physician, participants who are not candidates for PD1/PDL1 antibody systemic therapy are allowed * Any systemic therapy provided in adjuvant, neoadjuvant, or chemoradiation settings for urothelial carcinoma can be considered to be in metastatic setting, if the last day of treatment was within 12 months prior to the diagnosis of metastatic disease * Participant must have completed any planned surgery or radiation therapy prior to registration * Participant must not have unresolved toxicities from prior surgeries or radiation therapy \> grade 1 at the time of registration * Participant must be ≥ 18 years of age * Participant must have Zubrod performance status 0-2 * Participant must have history and physical examination within 28 days prior to registration * Participant must have complete blood count (CBC), complete metabolic panel including liver function tests, and lactate dehydrogenase (LDH) obtained within 28 days prior to registration * Participant must have adequate kidney function as evidenced by measured or calculated creatinine clearance \>= 20 mL/min within 28 days prior to registration * Participant must have adequate hepatic function documented by either aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 3 x institutional upper limit of normal (IULN) within 28 days prior to registration. If both AST and ALT are performed, both must be =\< 3 x IULN. For participants with liver metastases, AST or ALT must be =\< 5 x IULN * Participant must be on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 6 months prior to registration if they are known to have human immunodeficiency virus (HIV)-infection * Participants must have undetectable hepatitis B virus (HBV) viral load within 28 days prior to registration if participant has known chronic hepatitis B virus (HBV) infection * Participants with a known history of hepatitis C virus (HCV) infection must have an undetectable HCV viral load within 28 days prior to registration * Participants may have a prior or concurrent malignancy provided the natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen per the opinion of the treating investigator * Participants must not be planning to take strong or moderate CYP3A or CYP2C8 inhibitors or inducers if randomized to Arm 1 and standard of care (SOC) regimen chosen is paclitaxel or docetaxel. Participants receiving strong or moderate CYP3A- or CYP2C8 inducers must discontinue use at least 2 weeks prior to randomization * Participant must not have a known history of corrected QT (QTc) prolongation * Participants must not be pregnant or nursing due to the risk of harm to a fetus or nursing infant. Women and men of reproductive potential must have agreed to use an effective contraceptive method for the course of the study and 6 months (females) or 3.5 months (males) after the last dose. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate participant chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Participants must be offered the opportunity to participate in specimen banking as outlined * Participants must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system