You can remove items from your own home and keep/re-use them. You also keep items if you relocate. It's a general warning that if you allow others to have access and they take am item, then you no longer own it.

There are some items that will be destroyed upon removal, but you get a warning in-game before doing so. For example, if you remove an aquarium into your inventory, any fish or decorations will be lost but you keep the actual tank. Placing an item into your housing storage does not destroy anything.

If you want to place an item in more than one location, then you need to purchase multiples. They are a physical item.