The news comes way of 343 Industries boss Bonnie Ross, who revealed to IGN that if 343 Industries was never founded to take the reigns over from Bungie, Microsoft was either going to dump it onto the lap of Gearbox Software or just end Master Chief's story.
According to Ross, after Bungie left Halo to go work on Destiny with Activision, there was a period where the future of the series was really up in the air.
Halo 3's ambiguous ending was seen as a good ending to the series, but it also left the door open to do more. At the time all of this was happening, Ross was running all internal and external Xbox game publishing, and she personally felt it was "blashphemy" to end the Halo franchise and no longer expand its large and well-realized universe. She also felt the same way about handing it over to an eternal studio outside the Microsoft family.
Thus, she pitched her vision for the series to Shane Kim, who was Corporate Vice President of Microsoft Game Studios at the time. And apparently, Kim liked what he heard because Ross was given the "keys to the franchise" in order to pursue expanding the Halo series.
As a result, an internal team at Microsoft was formed under the lead of Ross, which would become 343 Industries. From here, the new team went on to build upon the franchise with Halo 4 and 5, and now is working on Halo Infinite.
But as alluded to earlier, almost none of this ever happened. At the time, Microsoft was toying with ending the Master Chief story with Halo 3, and letting Bungie expand the universe with new stories, such as another ODST game. But then Bungie left.
And so at that point, Microsoft was looking at temporarily giving the series to an external studios, and Gearbox, who worked on the PC port of the first game, was at the top of the list. But none of this happened, and from the sounds of it, it was chiefly because Ross didn't let it happen.