Every owner of heirs property is responsible for property taxes. How much they owe is determined by multiplying the size of their ownership interest with the property tax amount. For example, I own an 34% interest in real estate with a tax bill of $323.00. My share of the bill is $109.82. Whereas, my cousin's share is 4.3%. Their share of the tax bill is $13.89.
It's very common for co-owners of heirs property to fail to pay their share of the property taxes and any other shared expense. It's also very common for co-owners to pay for their nonpaying co-owner's share of the property taxes. Oftentimes, they do this to ensure the property is not at risk for tax foreclosure. When that happens, though, the nonpaying owner does not lose value in their share of the property. Instead, they legally owe the co-owner who paid on their behalf. The paying co-owner can seek enforcement for reimbursement through court, but they do not get a greater interest in the family property simply because they paid more than their share of the property taxes.