Former Half-Life franchise scriptwriter Marc Laidlaw has published what appears to be part of the Half-Life 2: Episode 3 plot on his personal website. Laidlaw left Valve over a year ago.
The text that was published on Laidlaw's personal website appears to be a modified version of a part of the original Half-Life 2: Episode 3 plot. Important names, genders, races and events have been slightly altered, likely to avoid legal issues.
In the published plot players can read that Gordon Freeman and Alyx Vance do indeed make their way to the Borealis in Episode 3 and that they set out to destroy the ship just as requested by Alyx's father Eli, despite requests from Dr. Mossman to return the ship's technology to the resistance.
The episode ends the same way as all the other previous episodes, with G-Man now appearing to speak with Alyx instead of Gordon.
Laidlaw ends the post with "you know better than I the appropriate course of action, and I leave you to it. Expect no further correspondence from me regarding these matters; this is my final episode."
The last lines could imply that Episode 3 would have been the last episode featuring Gordon Freeman as the main protagonist or that Laidlaw will not publish any other information regarding Episode 3 and that he expects either Valve or the game's community to breath new life into the franchise.
The ending seems to align with previous statements from Laidlaw that indicated that Episode 3 would not have been the end of the Half-Life franchise.
The last Half-Life 2 episode, Half-Life 2: Episode 2, was released almost ten years ago on October 10th, 2007. Valve has not released new Half-Life content since then.