Your DH needs to find out what's going on immediately, what debts they are, and what personal guarantees he's signed.

If he's agreed to be a Director he can be personally liable for certain debts like some types of over due tax, meaning he can get chased PERSONALLY for it.

From the ATO's webite:- ATO - Director Penalty Notices

Director penalty notices
Company directors have a legal responsibility to ensure that their company meets its pay as you go (PAYG) withholding and superannuation guarantee charge (SGC) obligations.

The director of a company that fails to meet a PAYG withholding or SGC liability by the due date automatically becomes personally liable for a penalty equal to the unpaid amount.

When a PAYG withholding or SGC liability remains outstanding, we may issue a director penalty notice, although this is only necessary to enable us to start legal proceedings to recover the penalty. Even without issuing a notice, we can collect the penalty by other means, such as withholding a tax refund.
Your DH needs to find out what's going on, and get some legal advice. Stat.