It depends on the tank and the species.
The tiny hitch hiker Asterina reproduce by splitting. They would have little problem with being chopped in half, but then they do it to themselves already
Things like sand sifter stars are generally slowly starving after consuming a lot of stuff in the sand bed. Like many other seastars, they in general will not take to spot feeding, and so little can be done to help them. It is always worth trying, but in most smaller (less than a 100 bare minimum) tanks they will die in about 9-12 months.
A star that is regenerating at least indicates that it has enough energy and nutrition to regrow that arm...half a body is a different thing.
Linckia stars, which also reproduce via arm drops, tend to starve in most smaller systems as well. Their survival seems closely tied to large amounts of LR (the opposite of sand sifters, where success is based on open sand bed and little LR). If healthy, they also will reproduce on their own.
Chocolate chip stars and relatives, which can all be spot fed, tend to do relatively better in tanks. Brittlestars also, in most cases, can recover nicely from loss of arms.