You ABSOLUTELY want to keep the old roots intact. They have fungi attached to them which will attach to your new roots. If the old fungi are 3 feet long, as soon as your new roots meet the old roots or fungi, you instantly have 3 more feet of microbial "root" to feed your plants with.

You need not concern yourself about the roots from plants that grew in that place last year.
Whether they will be digested in one year depends on how alive your soil is and the mean soil temperature. If you soil cools down below 40 degrees in the winter the soil bacteria stop working, so no those roots will not get digested during the winter. However the soil bacteria will work on them during the next growing season and any nutrients the roots would have (they will have lots) will be put back into the soil for future use.

Your new roots will grow around them, and the old ones will break down this season.

yes leave them there they will break down and in the mean time cause no dramas for new plants.

len

Here is a link that might be useful: lens garden page

Yep, I've been doing that the last few summers. Even the thick plants
like eggplant and tomato and corn I just cut at the base and leave the
roots to rot.

I hear what you guys are saying about the roots, but the roots have kind of glued together some of the soil. Now I suppose you can shake off most of that soil but its like the soil and the roots are glued together. I would think that you should take out the main root ball and I guess allow the smaller little root hairs that were further down or out to stay. What do you guys think?

Personally, I'd just plant the next year in between the old root balls and give the balls another year to decompose.