What would cause a 1997 cadilliac catera blower motor to stay running with the key off and removed from ignition?

Since the blower motor draws so many amps it cannot be controlled by a simple contact. Instead it receives it's voltage from a relay that opens to brake the electrical flow and makes to turn it on. The contacts in this relay can easily handle the current. Find the relay for the motor and replace it. It has pitted and is hooked closed allowing current to flow even after the key is shut off.