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While I can't tell you want causes this I can tell you this problem is called "run-on" or also called "dieseling." Do a search on dieseling or try these threads.
While it's not a fix to the problem you if you have an automatic you can leave the car in drive after shuting the engine off to help with the dieseling.
Many Vettes have anti-dieseling solenoids on the carb. It allows the butterflys to close tighter when the ignition is shut off. Maybe yours is not functional. Mine was dead so I did a bubba re-wire and got it working now.