@jeromecorey,
Their behavior will depend on what species they are of course, but in general, if you remove their food sources they (and most insects) will not hang around or reproduce. Also, a maggot cannot mature into an adult fly without a food source, so they must be (or have been) eating something.
The real question is, what attracted them in the first place, and can you find it and get rid of it. An exterminator wouldn't hurt. At least they will be able to identify the species and figure out what they are doing there.
What geographic area are you in? Is this in a cold climate or a tropical climate?