i have no idea if its common, but i'm sure it wouldnt be uncommon for someone to grow them like that in their tank for appeal to people.
as for feed i turn off all pumps etc and take cyclopeeze....squirt a tiny bit at the whole coral to give it time to realize food is around.....then after a while it'll start to open and then i go back in and squirt more at it heavier to make sure they get plenty of food.....try to make it a routine a 3 times a week or so...then it'll get used to everything and start coming out even if it senses it a tiny bit.