Traits in Question:

YOU'LL MAKE A FINE ADDITION: When Collector hits a lower point character with a close combat attack and his attack total is at least 3 higher than his target's defense value, you may place the hit character on this card. Collector considers that character as Collected as long as it is on this card.

I WON'T LET YOU ESCAPE: At the end of your turn, place an Exhibit token on each Collected character's card, and roll 2d6 that can't be rerolled. Each Collected character rolls 2d6 and subtracts the number of Exhibit tokens on its card from the result. If a Collected character's result is equal or higher than yours, that character's controller may place it within 6 squares of Collector with an action token and remove all Exhibit tokens from its card. Opposing characters can be given a power action to remove an Exhibit token from a friendly character. When the game ends, all Collected characters are KO'd.

Question:

What happens if all characters on the opposing team have been Collected?

2014 Rule Book, page 17:
Since your opponent wouldn't have any characters left on the map, the game would end. When that happens the last line of I WON'T LET YOU ESCAPE kicks in and all of the collected characters are KO'd and you would get their points.

Mbstoner is correct.

That's what I thought but couldn't remember where that line was. Thanks!