They do. Here is last year's email:

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We're sorry to say we couldn't accept your proposal for funding. Please don't take it personally. The applications we receive get better every funding cycle, and since there's a limit on the number of startups we can interview in person, we had to turn away a lot of genuinely promising groups.

Another reason you shouldn't take this personally is that we know we make lots of mistakes. It's alarming how often the last group to make it over the threshold for interviews ends up being one that we fund. That means there are surely other good groups that fall just below the threshold and that we miss even interviewing.

http://ycombinator.com/whynot.html

We're trying to get better at this, but it's practically certain that groups we rejected will go on to create successful startups. If you do, we'd appreciate it if you'd send us an email telling us about it; we want to learn from our mistakes.

Y Combinator Staff

Thanks for sharing. We're anxious to hear the result. Invited or not, I think it's a good experience to force oneself to tell the story of your business and be really honest about it.

Good luck to everybody. You all feel like a classmate to me ;-)

Thanks for sharing, this will ease some of my friends anxieties today.

Pretty cool, I was wondering if they answered us or not.