Sapphire was the same way with the bone. Here's what I did...
First, it looks like that is a rawhide bone, correct? Sapphire would get very possessive over those. I would give it to her, and when I tried to take it away, she growled and snapped!
Don't pet him when he's doing that. I noticed he was growling and someone was petting his back at the same time. That's encouraging him to be possessive.
Take the bone away. You'll probably get nipped a few times for a while
, but it stops eventually.
What I did next, and this will seem crazy, but it worked! lol I got on the floor and layed on top of the bone. If Sapphire came near me and the bone, I growled at her! I'd also use my hands to "bite" her neck. The bone was mine and she was not to try to take it from me. I was the leader, and it belonged to me. When she finally walked away and ignored me and the bone and played with something else, I gave it back. After that, she wouldn't growl or snap when I tried to take it. Once in a while she will, and I'll repeat the process, but it doesn't take as long for her to get the picture not to growl or snap.
I hope that helps!!
As for when people leave, I have no advice on that... Sorry...