Comment by thequux

It's been a long time since I've touched any of this, so the details have slipped my mind. However, the general idea was that there were two different exit calls in DOS: terminate and terminate and stay resident. The difference between the two is that the stay resident option wouldn't release the memory used by your application. Further, the interrupt table, which told the processor how to handle each interrupt, was in RAM and therefore writable.

So, what TSRs would do is overwrite one or more interrupts to point to a routine that would check if the system call in question was one it wanted to handle (eg, to add a hotkey it would grab the keyboard handler and check for a special set of keys before passing control back to the normal handler). Once that was fine, it would call the TSR system call and control would be passed back to the OS with the hook still in place