Be sure to leave one of your flyers with each shelter, but do not assume that staff will phone you if your pet should show up at their shelter. However, other people who may have found your pet may see your flyer and give you a call that they may have found your pet. It is your responsibility to make sure whether or not your lost pet is there. Remember the beauty of a pet has nothing to do with whether or not they are destroyed. When their time is up at the shelter their time is up.
Shelters have many pets coming and going daily whether by adoption or otherwise.
Kennel space is very limited. Be there to find him, he is depending upon you to do so. The shelter may be too busy when your pet arrives to have time to make that one call to you, and you and your pet may never be reunited, just due to not going to look for yourself. Your pet depends on you to come look. If your pet was stolen and you have strong evidence of this, call your local police department to file a stolen pet report.