I am lucky with my guy. Although he has attempted digging a few times and been told "no", he doesn't take advantage of my absence to pursue the habit. One exception was when I assume he was cold, and he dug his way under the comforter on the bed, managing to do some damage to the foamy we have on the bed to make it softer. (never assume the bed that felt soft enough in the showroom will be so when you get it home! 🙂 ) He has free run of the house and seldom abuses the privilege.
Obviously if the damage occurs when you are gone the only solution is to restrict his access to the things he is likely to harm. Or suffer the consequences. 😉