After the sale of public houses, who will own the property rights? Who will bear the cost of property management? What are the relevant legal provisions?

The law is not so detailed, but it can be inferred from other aspects.

The unit helps employees to bear the property fee, which belongs to employee welfare. Welfare belongs to the welfare that can be paid if you want, and you can stop if you don't want to, so the unit has every right to do so. In addition, from the perspective of housing ownership transfer, it is reasonable for the unit to stop paying property fees. The house is no longer yours, so if the unit continues to pay the property fee, it is equivalent to giving benefits to non-unit personnel, which is of course impossible.