My Pug dog is considered my property and even though I paid less than $100 for him in 2000, he is probably the only property I would shoot over.
As others have said, if caught in the act I would draw but I would only shoot if threatened. I would stand my ground as it is my land, my house, and my right to stand my ground there. If they ran away that's okay, but if they came at me or threatened me I would defend myself and my family with force.