What does it mean to go negative on exchange?
When you buy 0.0001 BTC, it's the same as buying anything that you could, but are not required to, sell in the future. You (on the books of the exchange, until/unless you transfer the BTC out to a wallet you control) are the owner of 0.0001 BTC. If the price declines [or rises], you have a so-called "paper" or "unrealized" loss [or profit], but that's just hypothetical until/unless you actually sell the BTC.

If the price declines [or rises], you are "poorer" [or richer] -- your net worth declines [or increases], using the current BTC market price as the value of what you own. But until you sell it, you just own 0.0001 BTC and there is no need to pay (or receive) any $US regardless of price changes in the BTC market.