He's not letting you know because he's hiding something big. "Trust me" says the alkie. "I'll never drink again. I'll never lie again. I'll never stick you with any debt."
I agree with this.
Alcoholics always lie. They are not trustworthy. And alkies get very vindictive in divorce. Even if he can pay, he may try to stick you with a portion of the bills just because he's mad at you.
This was my experience in a break up and seeing it before in his divorce.