Engine Run On

I own a '85 Chevy Caprice, and I have recently had some problems with the cooling system. We checked the thermostat and hoses, and all appeared to be fine. We did have a small leak that was coming from the bottom of the radiator, which appeared to be coming from the drain valve at the bottom. We started to lose fluid somewhere, but it was more than the amount coming from the valve. Worried that it was the gaskets, we pulled the spark plugs, but saw no lime build up on them. Then as the fluid was being checked and filled more and more, things were getting hotter faster and we started losing oil at a faster rate and plugs were showing more carbon, but still no lime build up on them. Then we got to a point that the engine heated to the point that when I got it home, I shut off the ignition, but the engine ran on for at least 30 secs after that. Is that a sign that it is terminal, and is there something can be done with it to bring it back to some use, besides replacing whole engine, cause I am working with a very limited income.

Thanks for your help and time.

Sprts