Actually microsoft bought Bungie while halo was being developed due to a recall on some games. One million games in fact back in 2000. Bungie got free in 2007 gave up what ever rights they had left to microsoft for freedom then departed. They made two more halos before leaving 343i and MS to carry on the halo franchise. Bungie has stacks of games they want to make.
Destiny is the result of those efforts.