The purpose of this study is to determine if relapsed chronic lymphocytic leukemia (CLL) will respond to mirdametinib and if this approach is better or worse than the usual approach for relapsed refractory chronic lymphocytic leukemia.

Mirdametinib is considered investigational, which means it has not been approved by the U.S. Food and Drug Administration (FDA).

Participants receive the study drug, mirdametinib, twice daily until their disease gets worse or the side effects become too severe. Mirdametinib is taken orally (by mouth). 

After completing the study treatment, participants continue to be followed and monitored for side effects for 5 years or until a new therapy treatment is started. Follow-up clinic visits will occur every 2 months until starting a new therapy and by phone call every 3 months after starting a new therapy treatment.