The starter disable is a simply a relay designed to interrupt the starter.
They cut the crank wire off the keyswitch and so power to starter is interrupted when alarm is on. Done by standard relay
In reality, a car alarm just interfaces with the battery for constant power, the keyswitch (only has power when car is running) so it knows it's being driven, (usually) one wire to know the doors are open, and two wires for hood and trunk, assuming they are installed. 3 wires minimum for a bare bones install.
There aren't really very many actual connections to the electrical system of the car itself. Alarm manufacturers are pretty specific about NOT interfering with circuits that may affect the vehicle during operation (like cutting a wire to the ignition coil or the fuel pump) because of safety issues.
Of course, there are dumb asses out there that do it anyhow just to be slick and stupid. Majority of the installs I have seen follow the book however, and only a ricer would do an alarm install like that on their car...
If you ever have to remove an alarm, remove the brain, shock sensor (usually zip tied to the steering column) siren, but leave any relays in place on the car. Reason being is if the car is starting just fine otherwise, don't try to remove the relay, you will just run a risk of creating an unreliable connection.
Leave the little black relays in place.
PS I like buying old Cliffords
I consider myself a fan of 'em. If I was in LAX right now I'd have it running in zero seconds.
rjp