They can. According to the Florida Department of Environmental Protection, the federal Asbestos NESHAP (40 CFR Part 61, Subpart M) sets work practices for demolitions and renovations of structures and buildings, excluding buildings that meet the residential exemption criteria in the NESHAP. Florida DEP administers the program under Chapter 62-257, Florida Administrative Code.
For buildings subject to the NESHAP, the regulations require the owner of the building and/or the operator to notify the applicable compliance office before any demolition or renovation. DEP's page says notice must be submitted at least 10 working days before the project start date, using DEP Form 62-257.900(1). Notices go to the appropriate district or local program compliance office, and Broward County is listed as a local program.
Whether your house is covered depends on the building and the project, so read the DEP page and contact the compliance office it lists before scheduling demolition. We don't accept or haul asbestos.