Banks do this all the time. Honestly, it is "poof! gone!"
In fact, I've done it within my business -- and in so doing, had a positive tax result! My accountant explained the benefits of discharging the debt at the end of the fiscal year, how it balanced my books and created a good re-set which made the business healthier.
I don't understand why people don't understand how this debt forgiveness/discharge stuff works. It happens *all the time* in all manner of consumer, medical, and foreclosure debt. That's what happens in bankruptcy court.