Accounts don't get banned, only the consoles.
So if anything you might have a worthless console then (which again is still a big IF), but the games that are tied to your account are still there.

Well, then they need to update their information because this is what it says on their site.

"Service suspension

Service suspensions are imposed because of inappropriate gameplay or system abuse. Inappropriate conduct includes these kinds of actions:

Inappropriate in-game behavior (scamming or cheating)

Attempts to manipulate Xbox LIVE services through network interference, feedback abuse, complaint abuse, or other system tampering

A service suspension completely blocks a member from being able to sign in to the Xbox LIVE service. The duration of the suspension depends on the frequency or severity of the offense. Temporary suspensions usually end at approximately the same time of day as when the suspension was issued."

http://support.xbox.com/en-US/xbox-live/account-banning-and-player-feedback/account-suspensions-and-console-bans

Huh, interesting. I know that in both Halo (100% sure of this one) and COD (90% sure of this one) you get banned from the game, not the service. I suppose there probably are a few games where you get banned from XBL totally. 

Although in the unlikely case of that I'm sure the Xbox will still do the automatic check up (unless you did something really bad) every 24 hours but you just won't be able to go on XBL.

Well, then they need to update their information because this is what it says on their site.

"Service suspension

Service suspensions are imposed because of inappropriate gameplay or system abuse. Inappropriate conduct includes these kinds of actions:

Inappropriate in-game behavior (scamming or cheating)

Attempts to manipulate Xbox LIVE services through network interference, feedback abuse, complaint abuse, or other system tampering

A service suspension completely blocks a member from being able to sign in to the Xbox LIVE service. The duration of the suspension depends on the frequency or severity of the offense. Temporary suspensions usually end at approximately the same time of day as when the suspension was issued."

http://support.xbox.com/en-US/xbox-live/account-banning-and-player-feedback/account-suspensions-and-console-bans

What if it is your account that they banned? When banned you cannot connect to your Live account.

That's not what happens on 360 and I doubt they'll change it.

Doesnt it seem pretty obvious that the x1 would have a different tos?  I mean, the 360 isnt a completely connected hardware platform like the x1 is.  It is pretty much guaranteed that the x1 bans would still allow people to online check and play their games, just not the multiplayer.

that being said, the sheer nature of the x1 would make it very hard to even get banned.  The drm'd nature of the software will prevent most piracy, which is one of the biggest reasons for getting banned.  

Not that i really care if people that actually get banned from their account lose their access, because xbl sends out so many warnings and gives users so many oppurtunities to fix or change their behavior before they are banned that i have no sympathy for them. At all.

There is your answer.  Kinect will answer your commands with, "The fuck you want, sub-human?  I don't take orders from trash."

Doesnt it seem pretty obvious that the x1 would have a different tos?  I mean, the 360 isnt a completely connected hardware platform like the x1 is.  It is pretty much guaranteed that the x1 bans would still allow people to online check and play their games, just not the multiplayer.

that being said, the sheer nature of the x1 would make it very hard to even get banned.  The drm'd nature of the software will prevent most piracy, which is one of the biggest reasons for getting banned.  

Not that i really care if people that actually get banned from their account lose their access, because xbl sends out so many warnings and gives users so many oppurtunities to fix or change their behavior before they are banned that i have no sympathy for them. At all.