Laolai 老赖 refers to those who can afford to pay debts but refuse the court orders to do so. High cost private school tuition is considered luxury spending. So the ability to afford private school is considered constructive evidence of ability to pay debt outstanding.
China needs to figure out a personal bankruptcy system. But it also needs to figure out how to deal with people who hide assets through friends and relatives.
As it stands I doubt this has much to do with social mobility, as some seem to be worried about here.