If you have suitable space it could be done - but usually not worth it (I would do it if I had a greenhouse). The determined variety or some bush tomatoes will not grow too tall, but could be pita to overwinter indoors. I am assuming you are in a apartment or TH - is there a sunny, warm place you can keep it? They need very good light otherwise will grow leggy and weak, and could easily get bugs. They would grow and produce if you can do it.

Buying a new seedlings in early spring is usually much easier and they are really not expensive at all. Or you can start them from seeds early, and have nice plants to pot up outdoors when warm enough (I start all of mine every year, and have at least 20 if not 30 varieties of seeds).

Saving it is not a good idea.

I appreciate it, guys. Even though I feel a bit sentimental about disposing of them (I babied them like children, & 2 little plants gave us 4 different batches of tomatoes over the summer!), I agree that it's probably best to let them go and start afresh in spring. Thanks again.