Bankruptcy doesn't make a U.S. citizen unable to apply for a K-3 or an I-130 petition. But he will need to be able to show compliance with the requirements of the I-864 affidavit of support, by which he and any co-sponsors would ensure the existence of available income at least 125% of the federal poverty levels.
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Yes, he can apply. The Bankruptcy itself does not stop him. However, if he does not make enough money and his spouse will become a public charge, then it would most likely be denied. However, you could always get a joint sponsor. Please see more below.