We sometimes like to talk about Nintendo going 3rd party -- however we can pretty much assume that won't happen if there's radical change in Nintendo management and the company goes broke (which would take a long while).
Sony on the other hand, in spite of the PS4's success, stands on the brink. As for the Vita, even with decent sales in Japan, can be pretty much considered a failed console and doesn't do much to contribute to Sony's bottom line.
I believe that could change if Sony treated the handheld gaming space differently. First of all, I don't think anyone would be surprised if we ever saw Sony move games to Android. They've basically done that in some iteration before and I'm sure they'll do it again. However let's talk about the elephant I left in the room: putting Sony franchises on the 3DS.
I know some of you are already typing 'That's a ludicrous idea! Shame on you!'
But here's my reasoning:
By introducing Nintendo handheld gamers to IPs and franchises they may not have had before, it bolsters the chance those very Nintendo handheld gamers go for Sony as their home console of choice in favor of Xbox or even *gasp!* the Wii U. Additionally, it'd support Sony with considerable new game sales. Certainly you could port LittleBigPlanet to Android, but price it more than $10? People would throw a fit. Additionally, you'd make so many sacrifices and major design revisions that you might as well create a whole new Android game. However a LBP Vita port on 3DS for $40? More or less easy done with predictibly good results.
Of course there's down-porting involved when you put a game like Uncharted on the 3DS. But would there not be chance for such a release to sell better than on the Vita? And ok maybe that doesn't work for an IP like Killzone, however it does work for others. Let's say you have a Jak and Daxter game and you had total freedom to put it on either Vita or the 3DS. Which version could realistically sell best?
And here's another possible upside for Sony, by stepping out in good faith as a 3rd party publisher on Nintendo's handheld platform, Sony undeniably would hold an upper hand in bringing Nintendo onto Playstation home consoles if the big N ever did face a major management shake-up or crisis that prompted them to go 3rd party. There's no denying Nintendo going down would be a major catalyst for PlayStation's growth, but only if PS is truly able to absorb Ninty's IP and legacy (which would be challenging, but it could happen)
Bottom line: If Sony can't build a user base from the handheld market with the Vita, they can certainly just as well build a better business by leveraging Nintendo's handheld gamer base. And while it appears extremely unorthodox, it'd ultimately contribute more to Sony's stake as a major player in gaming than the Vita ever did. Sony has almost nothing to lose, except for the Vita - which isn't much to lose if you ask me.
Flame shield up.
I predict NX launches in 2017 - not 2016