It asymptotes to zero, never reaching zero.
Eventually a single dollar becomes worth less, you cant buy anything of value with it, you then need $10, then $100. then $1000...
Not there yet, eg. you can still walk into a shop and buy items, like food, for a single dollar. But one day your ancestors will walk into a shop and not be able to buy anything for a single dollar.
We trust in the Government and Fed to ensure the drop in buying power happens in a slow, orderly way and not a fast collapse. But the way the national debt is rising so fast, going be $100 Trillion within twenty years. It is pretty scary stuff. If they cant raise enough tax revenues they resort to money printing and the value of money collapses much faster.