Can Children Claim Our Furniture We Are Providing?

Context.. My FIL has no money, gets very little in SS. Basically he has outlived his money. He has 4 real children, and my wife is a stepchild. He married my wife's mom when my wife was 24. So the steps haven't been in place a lifetime. Her Mom is dead. My wife and I own the home my FIL is living in. Always have owned it, my FIL never had anything to do with financing, name on title, etc.. My wife and I are paying the expenses there, total about $650 a month with HOA, taxes, and insurance. All we ask my FIL to pay is utilities. His children will not, nor do they help out with any of these expenses. We own the furniture in the house also.. can his children come in and claim pieces of furniture? Last thing I need is for us to be paying the expenses for 6 years and the kids can claim our furniture. Does something need to be written up with ownership of the furniture spelled out? Without it do I have the right to deny any claims for me and my wife's furniture also. We are about $40k in expenses for their father already. They don’t care..