I can't say in the case of an individual, but in MI if you have something stolen, say carpentry tools, and they are taken to a pawn shop and the shop owner buys them following the requirements of the Good Faith Law (ask if it's stolen, get a copy of a government issued id, and get a thumbprint), the shop owner is not required to return the goods and take a loss. He may sell it back to you, charging up to the dollar amount that he paid. So no, you don't automatically get it back from the person possessing it. I know. I had all my tools stolen a few years back and went through this.
Now, if the item is reported to the insurance company, and they pay out a settlement, the item belongs to the insurance company. You may be able to buy it back from the insurance company, but they are under no obligation to sell back to you. They have the right to sell it at auction for a profit.
Now, if the item is reported to the insurance company, and they pay out a settlement, the item belongs to the insurance company. You may be able to buy it back from the insurance company, but they are under no obligation to sell back to you. They have the right to sell it at auction for a profit.
