Overstay fine (Abu Dhabi)

I am on a visit visa, and offered a job in a hospital here in AD. I was advised by them that I need not do an exit for the changing of my visa. My visit visa will expire on Jan. 13, and as of late the HRD representative told me my new visa is being processed. If ever my employment visa will take a longer time to be released, who will be responsible for the overstay fine?