It's been long known that Valve contracted Arkane Studios in the mid-'00s to make a new Half-Life game. However, little was actually known about that project except that it was set in Ravenholm and that Valve canceled production before it was close to finished. Now, thanks to NoClip's most recent documentary, we have a clearer idea of this project that never came to fruition.
PC Gamer broke out all the nitty gritty details shortly after the documentary aired. This new game (which was reportedly going to be Half-Life 2: Episode 4) was considered to be more of a spin-off than anything else. The main reason for this is that it didn't star Gordon Freeman. The protagonist was Half-Life: Opposing Force lead Adrian Shephard.
All of the Half-Life games that were developed outside of Valve have had alternate protagonists, and Arkane's game would've followed suit. Gearbox Software made Opposing Force, Blue Shift, and Decay; they starred Shephard, Barney Calhoun, and Colette Green and Gina Cross, respectively.
Inventive use of tools would've been a main focus of this game. A primary mechanic for both combat and puzzle-solving was a nail gun used for stringing power lines to an active outlet, creating an electricity field for shocking hordes of zombies. A locomotion tool was a leafblower that's outfitted to allow Shephard to double jump. There's also talk of a chainsaw.
Shephard had a sidekick: Father Grigori whom Freeman encounters in Half-Life 2. The priest is experimenting with Ravenholm's undead citizens, taking headcrabs and cooking them down into drug-laced drinks. It, uhh, doesn't end well for Father Grigori. He'd eventually mutate into some sort of monster.
But, it was all for naught. Valve canned the project. Arkane founder Raphael Colantonio says he believes it was because the game would've required at least another year of funding, which was an investment Valve didn't want to make. There's probably truth to that -- but, knowing what we know now, it's tough not to think Valve canceled Arkane's Episode 4 because it had no intention of getting around to an Episode 3.