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He can quit his job and file bankruptcy all he wants.......it will not stop child support. Child support can not be removed though bankruptcy ever for no reason. As for his support he can request a modification since he is not working but since he willingly quit the job the courts can refuse to modify the order based on suspicion of fraudulently trying to lower support payments.
They also can court order him to get back to work. He will still be required to pay support even if he is not working. If the judge orders a modification this will lower the amount he is paying to her.
I would suggest that if she has any witnesses to him telling her he was quiting the job to prevent having to pay that she take them with her to court when he requests a modification of the order.