Last week, I had a chance to check out the Destiny alpha ahead of time, and enjoyed it quite a bit. Live during their E3 press conference, Sony announced that everyone who signed up in time, would be able to play the same alpha from Thursday until Sunday -- which was yesterday.
The thing is, you can still boot up the alpha and play it. Confirming our suspicions, Bungie tweeted out the following message, "There's a rumor that the Destiny Alpha might be extended to allow dangerous experiments. Play beyond the official close at your own risk!"