Looking for the current regulation(s) dealing with indebtness, any ideas on where to start?

I am not sure about regulations, honestly. As far as I know, there is no rule against being in debt. I think the real problem you are looking at is not debt, per se, but paying the debt. I was almost $300,000 in debt when I left the service - two mortgages and two cars, and a wedding ring. There were no issues because everything was being paid on time with no worries about paying the other bills (electric, gas, etc.).
When looking at the consequences of not paying debt, you can look at Article 134, which can be utilized for a Soldier failing to honor their debt commitments. Further AR 600-15 does cover indebtedness. But please be aware, it also covers Command actions regarding that indebtedness. There are things you cannot do (like provide debt collectors information).
Additionally, if the Soldier has a clearance (and most MOSs have at least a SECRET these days) you can start by addressing how it will (or could) affect his clearance.
Additionally, I would make sure to set that Soldier up with ACS. Every post I have been to, ACS has a financial counselor who can help work through getting back on a good footing.

Final word of advice on this is that I would strongly recommend approaching this as a team effort and a correctional (let's fix this) attitude than a punitive or coercive attitude. Many MANY Soldiers get in over their head by making poor financial decisions. We shouldn't immediately jump to a "you dun fucked up," but rather a "ooh, it looks like things got out of hand. Let's look at what we can do to help you get back where you need to be."