Uh oh, now we're going to have a war
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All players can always win the ante, whether or not it's consolidated. This is more apparent in an individual ante game, but the principle holds true in a consolidated ante game. In the sense of "winning chips from each player" the ante is never considered as being "from a player" even if the ante system has changed so one person posts it per hand.
So to your question, the BB ante belongs to the table once it's posted, anyone can win it. The pots are still formed the same way. The Main pot is 300 per player, a total of 900. The side pot is the other 200 from the SB and BB, for a total of 400, and the BB wins that because the SB did not call the full amount of the BB.
Now in the case of the BB being all in with the BB ante (and this is the source of controversy and many hurt feelings on PCF) the ante is posted first, and the BB after. If the BB does not have enough chips for both, he can win the entire ante, but only as many chips from each other player as he was able to post in the BB. If the BB does not have enough chips for the BB ante, he is eligible only to win the ante.
Again this is how it works in an individual ante game as well, but some people make very angry arguments that it's distasteful that a player can be all in and only able to win the ante. But again, the same player was eligible to win the whole ante in all the previous hands since the last BB without posting the ante, so it's a trade off.
But this case shows exactly why it should be that way. A player has the ability to win the full ante without even having enough chips for the small blind in every hand preceding his turn to post the BBA, so when he has to post the ante for the table, he has to post that first. And besides, it's a pretty simple strategy adjustment. If you are under the amount of the BBA, just move in 100% of the time in your UTG hand. Then you can win the ante, and any action you get on your chips.