Tonight, those in the audience watching The Last of Us: One Night Live were treated to a special scene that was not broadcast to the Internet. It was a scene Neil Druckmann wrote that takes place after the events in the main game. This scene does not appear at any point in the finished game.

No footage was recorded. It will never be shown publicly. If you want to read this, please note that this is a very significant spoiler as it takes place after the events of the game. I have warned you.

Spoiler: 
"So the big surprise wasn't TLOU movie teaser, UC4 gameplay, or a freebie to take home. It was a deleted scene acted out. It was from AFTER the final scene in the game. In the scene, Ellie is in her room at Tommy's place, listening to her iPod/CD player etc. Joel enters the room and wants to talk to Ellie. He brings out a guitar and sings a song(Troy Baker played the guitar AND sang in the voice. Fucking amazing). Joel shares a joke that he tells Ester, a woman he's now dating from the camp, with Ellie. "What's the bad thing about eating a clock? It's time consuming." They laugh, Joel leaves the room, and Ellie strums a string. End scene, end journey..."

Another take on the scene:
The scene takes place at Tommy dam one night 4 years later. Joel talks about how Tommy trying to get Joel hitched to a girl named Esther. El lies acting fairly distant, probably conflicted about joels lie. Joel then said he has a special gift for her and busts out a guitar. Then he plays a special song for her. Then he gives her guitar and promises to teach her. The scene ends with her striking a note on the guitar

Druckmann said that this scene is a goodbye to Joel and Ellie.
This information comes courtesy of this (ADDITIONAL SPOILER ALERT FOR THIS LINK) NeoGAF thread.