Yes, that happened with Home Makeover, the show from nearly 20 years ago starring Ty Pennington.
They'd locate a deserving family--as you say, usually one with tons of foster kids, some of them disabled--and then bring in contractors to build them a new house. The houses were spectacular. Unfortunately, so were the property taxes.
In the show's later years, they scaled back the homes, and also offered some cash to pay property taxes.