Resource Guarding
Mild resource guarding is extremely common among newly arrived foster dogs. The first sign is that the dog hunches over his prized possession, lowering his head and forequarters to the ground as if protecting its guarded object with his own body. He may give an approaching interloper a sidelong glance without moving his head, showing the whites of his eyes in a phenomenon dubbed "whale eye" by Sue Sternberg. If tested further, he may growl, snap, or even bite seriously.
Resource guarding most commonly manifests over a high-value chew, food bowl, or favorite toy, although some dogs also exhibit it around doorways, thresholds, sleeping places, and proximity to the owner. It's common among newly arrived fosters for two reasons: (1) most of these dogs have gone seriously hungry in the past and haven't had many (or any) toys of their own, and they don't understand that they've just won the jackpot in life and will now have plenty of nice things, so they guard their prizes ferociously; and (2) they don't have any real relationship with you or other people and pets in the household yet, so they're not as forgiving of intrusions because they have no reason to believe that you can be trusted that far.
Don't punish a dog for growling or forcibly remove his treasures when he warns you not to take them. Punishing him for growling only teaches him not to warn you before biting. Next time, he might go straight to using his teeth. Forcibly snatching his treasures teaches him that you can't be trusted and that he'd better be even more vigilant and ferocious about guarding his things next time, because if he drops his guard for a second you'll yank them away. Again, that road leads straight to a bite for you and a needle for your foster pup -- not a place anyone wants to go.
Luckily, mild resource guarding is usually fairly simple to nip in the bud. Once again, management is key. Feed your new foster dog all his meals in the crate and only allow him to have high-value chews when he's being crated for bed or while you go out. This is advisable anyway because it prevents him from being interrupted by other dogs or small children while eating and builds pleasant associations with being in the crate; that it happens to be the best preventative for resource guarding is just a happy accident.
Crating the dog during meals and while he's enjoying chews accomplishes two things. First, it reduces the risk that someone will accidentally provoke the dog into snapping or biting when he's guarding one of his treasures. Second, it gives the dog no opportunity to practice his misbehavior and develop it into a habit. If the foster dog learns that growling makes people back away from the things he wants, he has an incentive to growl more often and start guarding more objects. It's safer to keep him in the crate and just totally ignore any stray growls he makes while in there. Don't punish them, don't move away in response to them, just ignore them as if you didn't hear a thing and continue your normal daily routine.
Your foster dog may not need any more than that for the resource-guarding behavior to gradually dissipate on its own as he comes to realize that he's not going to starve and there always will be plenty of toys for everyone. However, if he still shows any sign of being reluctant to give up treasures on request, you can add Let's Make a Deal to his training regimen.
Let's Make a Deal
For this training exercise, you need a low-value toy or treat such as a dry biscuit. It should be something that your foster dog cares about just enough to notice and half-heartedly play with, but not something he likes enough to guard. When your dog displays some interest in the bait toy, say "Gimme" or "Trade" and offer him a small piece of something really nice -- cheese, a little chunk of hot dog, a bit of roast chicken, whatever he loves. When he takes the high-value treat, you take the low-value treat (which he will probably have dropped and completely forgotten about in the meantime).
After he eats the high-value treat, try to get him interested in the bait treat again. Scoot it along the ground, play with it yourself, or toss it from hand to hand and then drop it on the floor in front of him. When he sniffs at it or picks it up, say "Gimme" or "Trade" and once again offer to exchange a small bit of the high-value treat for the bait.
Gradually work up to more valuable objects (empty food bowls, empty Kongs, medium-value toys) and then, if you feel comfortable going that far and your foster dog is not showing any signs of possessiveness, the ultimate things he guards. Throughout this period you should continue to feed him only in his crate, maintain a strict NILF protocol, and work on relationship-building via positive training.