If it would lose 2HP from the EV drop, and you started at 1 HP, its HP will drop past 0 and roll over to the max value (65535), kind of like when you get a super high score on a video game and it roles back to 0.
Otherwise, if its the last guy in your party you can knock it out and still walk around.
It would be useless, except that you can send out an egg that way, train up an egg to get level-up moves applied, then hatch it.
Upon hatching all EVs and EXP it gained is removed (sent back to level 5) but it keeps any evolved status (You can hatch a level 5 Dragonite, now you know how Lance did it) and attacks it learned.