I don't understand why you would ask this question. On the individual level its obvious that some debts won't be. It happens all the time for a lot of reasons. So I assume you aren't talking about the individual level.
But on the macro level zero debt is a very bad idea and unless civilization collapses there will always be debt. Debt itself is a very good thing. Too much, and too little, of a good thing is bad.
So in either case all debts being paid off will almost certainly never happen.
> Does anyone even believe that the amount of debt will go down
In absolute terms due to inflation it always goes up.
> (that allows people to have negative amounts of currency)
You say this like its a bad thing. Debt isn't a bad thing. Debt allows people to own homes and cars and pay for education and invest in business. Debt means you are optimistic about the future.