How do you know they were mandatory deportable offenses? If it is not something obviously terrible like murder or rape or kidnapping, whether it is mandatory deportable, or even deportable at all, depends on the specific details of the case. Shoplifting isn't always deportable, but it can be.
It is not a mandatory deportable offense. Deportation for failing to file AR-11 is something they "may" do. But anything classified as an aggravated felony under immigration law (even if it's a misdemeanor under state law) brings mandatory deportation, unless one is successful at obtaining a waiver. Shoplifting can fall into that category.
http://www.uscis.gov/addresschange
Again, it's up to each individual to decide whether to apply now and see what happens, or go on living their life and hope nothing happens. But in either case, somebody with a potentially deportable crime should consult a lawyer to get a realistic idea of the potential consequences and risks (or lack thereof) of applying vs. not applying.
