Interest payments go to whoever holds the relevant debt security when the interest payment is made. But since the size of this payment is known in advance and the United States is (so far at least) a good debtor, this will be priced into the security before the payment is made.
In the case of T-bills, this is just baked into the price. The way that works is the US government says OK, a year from now we will give you $1000 for this piece of paper, now, how much will you buy the piece of paper for? And maybe they can find buyers for $985, so they get $985 now (which they can spend on stuff the United States needs, now) and they pay back $1000 in a year, by which time it's very possible that they've benefited by far more than $15 in practical terms.
If you have a generic investment that can't afford to accidentally fall in value massively overnight, but does need some liquidity, particularly if you're American, there's a good chance it's invested in buying these securities, whether T-bills, notes or bonds, because the US government has, so far at least, been good for the money. For example if you're going to need your pension funds in two years, you can't afford to have them tied to the NASDAQ just as the dotcom crash smashes it, but Treasury notes are a much safer place to keep it, even though say MSFT _on average_ makes more money over a long time.