New Fox has a lot of Disney dollars right now, and they're in a position to BUY something that is more modern and less tied down to the past. They actually have the cash to buy both Viacom and CBS, if that's what they wanted to do. My sense is they're looking for a more modern 21st century production operation to buy.
But, who could that be? Lionsgate? Don't see that happening. They could buy a smaller studio, but I am guessing that they signed a non-compete as it pertains to studios for a certain amount of time.
What I could see is someone buying what is left of Fox. It's valuable still, even though they don't own any actual content anymore. I'm thinking someone like AT&T may want to add broadcast/sports to it's roster of assets. They already have strong production assets, but have no broadcast resources to get them to the "cordcutters". They already have a news arm with CNN though, so Fox News couldn't be part of that deal. Disney could have taken Fox News, but I am guessing they didn't want to make the political statement that Fox News has aligned itself with. This would also solidify AT&T with sports.
Comcast already has NBC, so they'd be out for what remains (unless they wanted to make a play for Fox News while the rest goes to AT&T).
CBS would be out, as they already have a news play, and a broadcast network. Viacom, as stated, could be interested. We also can't rule Netflix out, they certainly have the money, and it would get them into sports in a big way (should they see that as needed). Amazon may also be interested.
I can't see why Fox would have gotten out of the cable/studio business if they wanted to stay in it long term. Cable networks are dying, so to be competitive in that space you are going to need a strong streaming platform, and nothing has been proven as to what the market will bear for those. So far, consumers seem to be fine with larger library streaming services, but reject anything specialized (SeeSo, etc). I think studios are hurting as well, as fewer people go to the movies and opt instead to use the nice setups that most have at home (again, another reason for streaming/VOD).
I really think that Murdoch saw this as the right time to go out, before things lost too much value. Serves as a nice retirement for him, and will take care of his family. I think if he could have, he would have divested Fox/News/Sports, but saw that as a non-starter with regulators (and the only other interested party, Comcast, also has no room for these three groups). I think if they intended to stay in the business of sports they would have held on to the regional sports networks, or tried to buy them back when Disney couldn't take them. (But again, I see those as part of the dying cable business, so they will only lose value and eventually money as they can't pay for those sports contracts with fewer and fewer subscribers).
Or, Fox could have decided to hang on to the properties they think still have growth opportunity (Fox being available for free with an antenna in most areas). Another possibility is a sale to Sinclair. They don't own as many TV stations, so less to divest, and they already expressed an interest in getting into conservative news.