I like what you say about the subject.
"But when we forgive someone, all that means is that we have assumed a debt that they are unwilling (or unable) to pay."
If I may offer...
I tend to think of it as more like canceling a debt that is owed me when I forgive it. I don't actually assume their debt to me as an unpaid debt that I now owe someone else. Either way, the end for me is a peace of heart and mind that I cannot achieve if I am still holding that debt over someone I cannot reach for accountability.
Money talks ... but all it tells me is 'goodbye.'