Curly slings are known to dig and burrow a good deal.
If you would like to try feeding, feed a cricket or roach that is no bigger than the size of the Tarantula's body, in other words the distance from the fangs in front to the spinnerets at the rear, in fact prey smaller than this is better (if it's a sling, but if it's quite large already just feed anything that it can handle easily), and chuck it in with your T. If the food is still there the next day, take it out and try again in about a week.
What you need to watch out for is that T's sometimes close themselves in so they can molt, and you don't want live prey wandering around that could harm your T in the middle of a molt. It could also be burrowing because it just wants to feel a bit more comfortable with its surroundings before it ventures out and about. A good supply of food is a nice way to make your T feel at home
HS