Well, they would get unpatched games which won’t be playable anyway 😀
But no, this only happens for downloaded game, and even then it’s generally for games you have downloaded as part of subscription. If you stay offline for long period of times (don’t know exact time these days, but I think it’s at least more than a month), then PS needs to recheck if you still have the subscription, or if the game is still present in subscription.
They had many options, could do Xbox 4 after 360, that would have been easiest, but maybe they didn’t want people asking why they skipped 3.
They could also do 720, then 1000, then 2000, and so on. Would still be a bit confusing when compared to 1, 2, 3, 4 but you would still know that largest number is the latest.
After Xbox One, they could go Xbox Two, but maybe they felt it has same connotations as PS3 vs Xbox2.
What I am really curious about is, what will they name the next Xbox? It also makes me feel for them. Just because they came a generation late, they have to spend don’t know much resources every generation just to come up with a name, whereas PS can just increase the number (and no, we aren’t going to talk about Nintendo in this 😀 )