This is a copy-and-paste from the Miami-Dade board:

FSS 30.15 appears to cover the statutory duties of a Florida sheriff:
http://www.leg.state.fl.us/statutes/...s/0030.15.html

FSS 30.15 specifies that a Florida sheriff must:

(a) Execute all process of the courts and county commissioners.
(b) Execute writs, processes, warrants and other papers directed to them.
(c) Attend all sessions of the court.
(d) Execute all orders of the county commissioners.
(e) Be conservators of the peace.
(f) Suppress tumults, riots, and unlawful assemblies.
(g) Apprehend any person disturbing the peace.
(h) Have authority to command any person to assist them in the execution of their duties.
(i) Be timber agents.
(j) Perform other duties, as imposed on them by law.
(k) Establish, if the sheriff chooses, a Guardian Program to prevent school assailant incidents.

FSS 30.15 says nothing about running a jail or a patrol division (so those appointed directors may remain in their positions, at the discretion of the county commissioners). A sheriff's primary statutory obligation is running the courts, serving papers and obeying the orders of county commissioners. Thus, the Miami-Dade county commissioners only need to fund a sheriff to operate the courts, in conjunction with other minor duties that are listed above i.e. timber agents, etc.