Generally, the property rights bought after 1995, no matter who pays for it (the cost of buying this kind of house is very low, and whoever pays for it doesn't mean anything), belong to the person registered with the real estate license, so the property rights belong to the children. Because at that time, parents can ask to write their own names, if not, they can only agree to give their shares to their children.
If it was stipulated at that time that only one person's name could be written when buying property rights, then the current law can support parents' request to re-write their own names to safeguard their rights and interests.
There is no relevant law indicating that this kind of property is a gift from parents, but because the original source of this kind of property is indeed welfare housing distribution, it is distributed by the parents' unit, which also solves the housing problem of the whole family. Therefore, in this kind of property, even if only the children's names are used, parents still enjoy the right of permanent residence.