Quoting: Bobcat205
my theory is that Bettman will buy the team himself and the team would be owned by the league (much like the New Orleans Hornets were in the NBA for a time) just to keep them in Arizona (likely by giving a bunch of money to the city of Glendale to extend the lease to Gila River Arena). He's gone this far to keep them in the desert, why not go farther?
I wouldn't be entirely surprised by that, but I don't know if the NHL really wants to take control of the Coyotes again. When they owned the team for 2009-2013, they Coyotes had some success during that time, and the increased fan support from that time, in my opinion, helped to sell the team to a buyer that was willing to stay in Arizona. Since the Yotes don't have that type of support now, I see the NHL having a much harder time justifying sinking the necessary amount of money to keep Arizona stay put.
I also think they will be more willing to consider a move to Houston as it still satisfies Bettman's desire to expand to southern cities. Houston is (if I remember correctly) the 4th biggest city in the USA, meaning there are plenty of possible fans to draw from, and is also located in the south, which has seemingly been a point of interest for Bettman.
Finally, remembering back to when the NHL was looking for a buyer, I don't remember there being any interest from outside groups other than from True North, who obviously wanted the team to move to Winnipeg. Now the NHL has a potential owner in Tilman Fertitta, who is willing to pony up the capital required to make a team in Houston work. I do think we could see the NHL owning the team for a season or two perhaps, but I think Bettman might finally be willing to give up on the Phoenix experiment. The only thing I can see the NHL doing that might work would be moving back into Phoenix proper. But even then, I'm not sure that would be enough to save this team.