Besides Asterina, true seastars don't do well in small tanks. They don't generally do that well in large tanks, but there is at least some hope for them there. The diet of most of the stars in the hobby is unknown and very few of the reef safe species take to spot feeding.
In a 10-20 gallon a small brittle or serpent star would be ok as long as you fed it meaty food occasionally and made a special effort to keep your salinity constant. Most echinoderms are pretty intolerant of salinity changes, so you would have to work to keep on top of evaporation in such a small tank.