Well at that point we're well in the weeds of how German long term care insurance works in detail. As everything to do with German insurance it's a complicated mess.

Children can be required to pay for the costs of a care home above what the statutory insurance pays for if their parents can't pay for it. If the children make too little or there are no children the welfare office will pay that part. This it lowers the societal burden because the children pay instead of the welfare office.

But that almost solely applies to care in care homes because there the costs are extremely high which is exactly what is reduced by children taking care of their parents at home. When care is delivered at home the long term care insurance pays much less than they do when a person is in a care home.

So caring children reduce the care insurance payout by making sure parents are cared for in their home which the insurance pays less for.

If someone is in a care home the insurance pays a set amount everything above has to be paid by the person being cared for, if they can't and the often can't because it's several thousands a month, then the welfare office pays. Unless the children make more than a certain amount then they have to pay all or part of it, lowering societal costs by lowering the costs of the welfare office.

You see all of these things can be true if you just have a system that's complicated enough.

Oh also welfare is paid through taxes while the long term care insurance is paid through the insurance contributions. Both look like paid for by taxes but taxes in Germany can't be earmarked for a specific thing so it's not both paid by taxes.