If something happens to other people's belongings, whose responsibility it as far as replacing it would be concerned?

Depends on what happensif a fire or water, the owner if someone steals things, then the thief unless a door left openusually you store your belongings at your risk.

They are allowed to store their stuff as tenants/invitees of your aunt. Thus your aunt is potentially liable. Your aunt should have homeowners insurance to cover the personal property.

All parties should have appropriate insurance, homeowner's or renter's, whichever applies. It should be clearly understood that everyone is bearing their own risk of loss, if they chose not to insure.

This is a "buyer beware" situation. Each person would be responsible for their own losses unless you or one of the other co-owners agrees to be liable for damages, or someone intentionally damages the property of another. Usually landlord are not responsible for damaged personal property unless they were on notice of a problem and did nothing to repair it. So if there is a ton of stuff in your basement and a sudden water leak breaks out, you are not liable. If you saw a pipe leaking or you were told by someone that the pipe was going to burst and you do nothing about it you may be liable if you entered into a landlord tenant agreement with the people who moved in.