What do programs do when they are Stopped in Unix / Linux?

I’ve been using Linux since 1995 and I have a little knowledge about processes and the lot; My question is, if you suspend (^Z) a process, I know it is given the STOP message but then what; does it just wait indefinitely until you do something else or does it all depend on the internal coding of the particular program i.e. does the program have to handle the STOP for memory management, etc?