Are you familiar with marginal analysis from economics? This is how markets work for everything. You are considering the one person with no TP, paper towels, or soap -- that is the person who will not be dissuaded from buying at any price. But there is always one person right on the edge of buying at the current price -- one who has a single roll left and can stretch it, or one who can just poop at work, or one who grew up wiping with corncobs and always thought of TP as a luxury anyway.
As the price goes up, those people drop out one by one. It is those marginal consumers, not the one who needs TP the most, who are price sensitive. This ensures that the person with no TP, paper towels, or soap is always able to get the TP that they need now. Even if there's only one roll left. The price may have to rise to $100 a roll to distinguish between them and the next-most-marginal consumer (who also has no TP, paper towels, or soap, but is willing to hold their poop for a day to save $100). That's the most efficient outcome and markets are great at finding it.
