Rick, Illinois has such a large population with a corresponding large number of registered vehicles in the state, that it was a simple case of they ran out of numbers when every vehicle simply received a next-number-in-line plate. So quite some time ago now, Illinois created different vehicle catagories, so that with either a prefix or suffix letter on the plate to designate the class, the same number could now be used multiple times.
That worked fine for awhile, but as the state's vehicle population continued to grow, the state became close to running out of numbers again, so classes were broken up even further. The most obvious example of this were trucks and trailers that were broken up into sub-classes based on their weight.
But in keeping with what we're interested in here, the state created a "For Hire" class that included taxis, limousines/livery, and funeral vehicles. When that class got broken up, taxis received plates with the letters TX, livery received the letters LY, and funeral vehicles received FH, which literally stands for funeral home. And the FH plate can be issued to any vehicle that is owned by a funeral home, not only the hearse. And likewise, you need to be a licensed funeral home with the proper proof of insurance in order to be issued an FH plate.