the Sand Sifting Sea Star should be actively fed a varied diet consisting of natural food sources, especially in well-established marine aquariums. Otherwise, this voracious feeder will quickly clean your aquarium of detritus and then burrow into your substrate, starve, and eventually begin to decay.
That's from liveaquaria. if you just let them be then yeah they will starve but if you feed them they will thrive but you should start feeding them soon as get them or they might hide and starve if it's a new sand bed.