Rescued Lab

Question
I rescued a lab from a kill shelter two days ago. He was picked up as a stray, so i know nothing about his past. He is very well behaved. He can sit and shake and doesn't jump on people. He only has one issue- food. He does not have any food aggression, he only eats everything he can find. He digs in the garbage for it, he will stand up on his back feet to get any food on the counter or the cat food on top of the dryer. I have an 8 year old lab who is used to just having his food out and he eats whenever he's hungry. Obviously, this is not happening for right now. Will this behavior change once the new dog realizes that he will be fed on a regular basis and settles into his new  home? Is there something I can do to help him realize that? I have two small children, ages 2 and 4, and I don't want the dog taking their food. He has not been aggressive about taking it from them, but he has done it already. He's very gentle when he takes it from them, but I'm afraid this will continue and he'll be a nuisance to people when we have get togethers. Thanks for any advice.

Answer
Unfortunately many Labs eat like they are starving.  The one you have may not because it is getting more than it needs, see  http://www.longliveyourdog.com/twoplus/RateYourDog.aspx

The only real solution is to keep anything he might eat where he can't get it.  That is a bit of a problem with little kids.  He may also chew up their toys.  

This might help:

Counter Surfing

Does your Foster Puppy counter surf; constantly checking the tables and counters for a tasty morsel that he is sure was left there just for him? If so, teach him The Can Can! For The Can Can you will need about 6 cans (empty pop cans with a few rocks or pennies inside them and a little piece of duct tape over the hole works well). Stack the cans in a pyramid on top of a piece of cardboard or paper to which you have attached a piece of string. Tie the string to the object that your Foster Puppy most desires from the counter top. It may be a dish towel or if it is food he is seeking, use a paper towel that you have used to pat down a piece of meat or maybe some meat juice. Then wait. When the object is snatched from the counter top the pyramid of cans will come crashing down, startling the thief. Your puppy will be caught in the act red pawed! You have just created a self correction! It may take several repetitions to get the point across, but soon your puppy will decide that it just isn't worth taking the chance.