some starter relays may "stick" on and not release when the power is cut from the switch. The other possible is the switch gets stuck on, even though the key will turn and come out as "off". Check both of those.
Three weeks ago I went out to start my 1997 Pontiac Sunfire. It started the car, but continued to crank after cutting the car off and removing the key. It continued until it drained the battery completely.
I put in a brand new battery, new alternator and new starter. The car ran fine for three days, until tonight. I left work and went to the store. As I was about to leave the store, the same issue begin to happen again. Luckily I had the tools to cut the power and not do any damage.
I waited 20 minutes, started the car normally and was able to make it home with no issues. I then started the car 20 more times in the driveway and it started the car normally.
I am all out of ideas and truly need some help with this issue. This is the only issue I have had with this car and has become a major headache for me.