Madden NFL 09 was the last game to come out for the Xbox. Microsoft shut down their servers a year after the last game for the Xbox came out.
Madden 09 would've released in Summer of '08 so it was closer to 2 years. But it's still a valid question.
And maybe someone went over this already, but Major Nelson said they wouldn't be bricking consoles when the day for shutting down XB One's Live service comes. I'm positive they wouldn't go that route. But the details could be sticky, especially with older (by then) consoles that might not be getting frequent use anymore.