99 Toyota Corolla

About 99% sure it is not possible.  The inherent obstacle is that the cassette player uses a data protocol that aftermarket head units cannot interpret.   Are the controls for play/ff/rew, etc. on the cassette player itself? or are they on the main stock stereo?

In theory, if the controls are on the player itself, that means that all that's going through the cable to the stock stereo is a low-level audio signal.  You could theoretically cut into the wire and find the correct wires for left, right, and signal ground, and solder to RCAs. then connect to an auxilliary input adapter for the aftermarket stereo.   Obviously that's a lot of work and probably not worth it for a cassette player.

Just out of curiosity, is this vehicle one of the model years where the corolla is a twin of the geo prizm?  If so, it uses that funky gm harness, and probably a delco tape player--which might be slightly easier to use with an aftermarket stereo.  still it's not gonna be easy.

i agree with whut ethan said..maybe suggest to your customer a double din cd/cass. had the stock unit been a am/fm/cass in one, not a problem. good luck lad.

my bad, 99 corolla only has single din up top and single a bit lower in dash right?