Game Over

I dunno, maybe sell the division to Samsung or Amazon and hope they revive Xbox' 1st party?

I dont see current MS management ever taking good care of the brand.

Nothing for 2,3 years
I think the sucess of xbx wont do any changes on their plans, maybe only the release date of xbox two.

They support it and come out with Xbox One XX while still supporting it.

It's going to sell a handful, that's it.
NA only maybe or just pull out, doesn't sell anywhere else.

Maybe by some miracle, next gen they manage to grab some new exclusives.

Xbox (insert some confusing name)

So in other words, your scenario is what most people expect to happen. Answer: nothing changes.
MS Xbox division's existence and profits do not depend on outselling Sony. 
Sony can increase their sales 10X and MS will still be doing the same as far as they are concerned re: Xbox.
It is not a Roman Colisseum gladiator death match that hinges on the outcome of who "beats" who.
AFAIK Xbox is doing well compared to previous gen (launch aligned), and has been consistently profitable per console (vs RROD etc).
If it ends up a globally limited brand that only does well in provincial, backward USA, well so be it, there's still $ to be made there.

Haha. Imagine telling him there are plenty of PS gamers who play neither sports games nor "Japanese" games.
But for sure, plenty of people are happy playing Xbox, particularly in MS' core markets.
And while people looking at big picture now see Sony as dominant console of the gen, people living in Xbox bubble don't necessarily.

For them, or their friends who are just now buying a current gen console, Xbox is the majority brand you buy to play with your friends.
That doesn't hold on a global scale, where many more people view PS that way, but it CAN be true in Xbox dominant markets.
Likewise, Xbox fans tended to over-estimate 360's dominance because if Xbox fans tended to live in 360-dominant countries.
(and merely conversing in English language is factor which skews the sample towards Xbox-friendly markets)
And in the big picture, that is fine, because "the global trend" is irrelevant to people's enjoyment of the games they choose to like.

XBox PC gaming service

Release XBOX ONE SEX which will be a fully VR based porn machine. That will sell imo.

As i said before, they need to have an alliance with another provider like Nintendo/SEGA or just a rebrand (less likely to work) or exit the hardware market.

Like atm it makes little sense for them to make their own hardware. As third party they would probably make more money.