Upon being chaptered out of the military, if there's debt incurred through CIF and a bonus, how does finance want them paid back?

Don't worry, Finance will get that money back via debt on your final check and Withheld Tax Return(s)

A portion of your final pay will be held for any outstanding debts. If that doesn't cover all of your debt, it will be passed to the treasury department and your IRS refunds will be confiscated every year till it's paid. I believe they also charge interest at the federal rate during that time.

The amount you owe will be based on the pretax value of your bonus, not the amount you receive. So, if you were paid a $10k bonus and received $7,800 after 22% tax, you'll pay back the $10k. You'll have to file an amended tax return for the year you received the bonus to recover the taxed portion

Way back when, there was a PV1 who had a little more than 3 years in. He was the DUI king of the BN.
He was so bad that the battery commander had to confiscate his car.
Anyway, after his final DUI the chapter paperwork finally came through, I was one of several who were tasked to take him thru out processing.
I took him to CIF and he had about half of his TA50. Of course it was filthy, and it was rejected. His reply was take it or don't, he was leaving in two days with or without a stamp on paperwork. In retrospect, he wasn't wrong. He signed a statement of charges.
Two days later, he was gone. (His getting his car back was a whole other story)
I kinda forgot about him until a few years ago when he finds me on F/B.
I chatted with him briefly. He sobered up, after he did a stint in jail ad then rehab.
I asked him what ever became of the TA50 statement of charges.
The Army took what they could out of his final pay. A couple years later, he got a letter from the IRS and they withheld his tax returns for couple years and then it kinda just went away.
Now, those were his words.
I don't know what happens in real life, but I'm sure the Army and the IRS will have a chat.
The government will get theirs.