What is the ruling on the thief's family benefiting from stolen items—such as chairs and desks—while knowing that they were stolen from public funds? Is there an exception that permits stealing public funds in this manner?

It is not permissible for someone who knows about the theft of these items to benefit from them. The duty is to advise the thief and urge him to return them to his workplace. If he is unable to do so, then it is permissible for him to donate them to charitable causes and public welfare. There are no exceptions for stealing public funds, except in cases of extreme necessity to avert destruction.