Hey,

I have seen this.  It is resources guarding.  Of course you know it is fear based.  The dog is fearful that you or others will take its meat. One thing I've done  was to only feed the dog from my hands.  This is so the dogs associates that I'm there to give and not take. Basically I'm not a threat.  Also the other purpose is to let them know that the only way it will eat is to behave calmly. If the dog growls or show any signs of aggression I will ignore it and walk away.  It won't eat today. The dog learns that if it growls, etc it will be ignored and no food.  Soon the dog won't growl. Then it gets to eat.

The other thing that I've done was use an e-collar. The dog has the leg quarters.  I come near or a family member comes near. It growls or looks funny. Then without saying a word  I push the  button until it stops. Dogs learn by association.  It begins to associate the low level stimulus with it's own actions.  It turns the collar off when it stops the behavior. 

I hope this helps.  Let us know about the progress. Like others mentioned this behavior needs to be quickly dealt with or I can get worse.