I ahve heard of this kind of thing before when debt collection agencies harass an ex-pertner (not even a marital partner) for debts owed by a third party. It seems that yours is the only address they have that has any connection with her and so they latch on to it. Try returning the mail to them, marked "not now or never at this address"
As long as he was not a co-signatory to these debts, and did not stand as a guarantor he should be OK. Sadly people often stand as guarantors for family members etc without fully understanding that they must take responsibility for the debt should the other person default.