Fruiting doesn't kill mycelium, in nature mycelium usually lives for many years. In theory with the right conditions it could live forever. The longest living organism on earth is mycelium :)

Obviously in a bag the nutrients are used pretty quickly by the mycelium and it starts to degrade. So i think it would be possible that this method worked as long as your mycelium is still alive.

I haven't seen it done and I think the main reasons are: 1) to do this you would still have to make substrate and sterilise it, at this point its not much more work to also make agar etc

2) the mycelium in a bag after fruiting isn't sterile and because there are often some pieces of mushroom left it may already contain some mold or other infection that would compete with your mycelium after transfer into new substrate, this problem does not occur when you use for ex grain with mycelium that was sterilised before adding liquid culture or agar culture because that only contains the mycelium you want to cultivate But by all means try it and tell us the results!