How can the purchase cost of a treasury bill be more than its face value?

Question

I'm considering (non-competitively) purchasing a 52-week Treasury bill through Treasury Direct. As I understand, the purchase price is reduced by the discount rate and therefore is always less than the face value of the bill. So that if I purchase a bill for $1000 at 5% discount, I would expect to pay $950.

However, TreasuryDirect gives the following information when purchasing a bill:

I understand that the total cost for my security purchase will be determined at auction through competitive bidding, and that the final cost of the security will not be known until after the auction results are announced. I agree to pay the full purchase price, which could be less than, more than or equal to the principal amount I indicated above and that full payment must be made on the security's Issue Date.

Could someone please explain to me how the full purchase price could be equal or more than the principal amount say if I purchased $1000 and the discount is 5%?

Edit: As per comments below, here's a plot of the 1-year treasury rate that shows near zero return during height of covid. It briefly became negative at one point in March, 2020.

Answer 1

The discount is determined at the auction, no-one guarantees you the 5%. You may end up paying more than the face value if at the auction the discount becomes negative (i.e.: becomes a premium), which is also referred to as "negative interest". While highly unlikely, the warning tells you that if it does happen - you'll be on the hook for the money.