It is on the attacker's red dice, not the defender's green dice.
Card Text: When defending, you may receive 1 stress token to choose 1 attack die. The attacker must reroll that die. If you have at least one stress token, you cannot use this ability.
Usage in game: When you just have to get rid of a particular die result.
MetalBikini's Breakdown: "I think Elusiveness is one of the more interesting upgrade cards of Wave 2. Although folks have definitely noticed that there are some builds, especially some Han Solo builds, that generate hits at a staggering rate, what might be equally interesting are some combos with Wave 1 and Wave 2 stuff that yield ships that are ridiculously hard to hit.
So Elusiveness just forces a re-roll, it doesn't flat out negate or mitigate, what's the big deal? First thing that jumps out at me is it's one of those, "When defending..." type cards. It's not an Action, it's solely up to you when it triggers, which is handy as you could conceivably take a hit or two from a primary weapon if you were out of shields, but if you see a crit coming down the road from a Heavy Laser Cannon or there's an A-Wing lurking nearby with Homing Missiles and Deadeye or something, you could hang onto it apply it then. Again, it's not a sure-fire way to get out of a hit or a crit, but for only two points and the fact that you can apply it to any attack die result, it ain't half bad.
The downside is generating a stress token for yourself, but look at when you're generating that token- the combat phase. You've already declared your Action for that turn, so as long as you pull a green maneuver in your next movement phase, you're not really incurring any penalty for using this card.
I think the key to using Elusiveness to its full potential will be to apply it to someone who is already difficult to land hits against for some reason or another. I don't think it's quite reliable enough to just tack onto just anybody and feel like you're definitely in better shape than you were before, but paired with somebody who's already a hard target? Especially someone who maybe doesn't have a no-brainer Elite Pilot Skill already associated to them?
Take for example Darth Vader. Two actions per round, one of which is an Evade. Stick Elusiveness on him and if you're Focusing as well, you've got the Focus to try and mitigate hit dice, you've got the Evade token to burn, and now you've got Elusiveness to re-roll whatever might have made it through all that. As early Wave 2 meta seems to be placing a premium on higher-point individuals rather than lower-point swarms, this would fit in nicely with most any Imperial list. If you really want to make things interesting, stick a Stealth Device on him as well. It could work on the named Interceptor pilot Turr Phennir with his boosting out of the way after an attack business too.
I'll tell you who I think could conceivably make the most use of this though, and that's Luke Skywalker. Dig this combo for a moment-
(37) Luke Skywalker + Elusiveness + R2-F2 + Shield Upgrade
Could anybody reliably kill that? You've got Luke's built-in Focus-lite ability, amplified by R2-F2 or just an actual Focus. For the hits that still land, you can force the opponent to re-roll one of them, then if it still make it through all that, you've got an extra shield. Holy mackerel. Or if you feel that's overkill, maybe shave a point and trade in Shield Upgrade for Stealth, or perhaps just leave the ship mod off entirely and save the points. Of course, with that many points you're likely locked into a strictly starfighter force, but hey, you gotta break a few eggs to make an omelet, right? Oh, and I know, I already hear it- "Oh, but he's got no offense." Fool-, he still flying an X-Wing, man.
Still though, much like our discussion on Y-Wings being inherently better to take R5 Astromechs than X-Wings because they have more hull and will likely be cruising around with crits longer, YT-1300s and Firesprays would make great use of this card too for the simple fact that they have more hull and shields, and are therefore more likely to stay alive long enough to use this upgrade a bunch of times. It doesn't mesh up particularly well with any of the pilots of these ships, but if I were coming in at 97 or 98 points and hadn't stuck on an Elite Pilot Skill, I'd consider it if I'd had trouble keeping one of those big ships alive the past few games. I still believe in general one should exploit that huge base on an area buff type EPS, but again- it'd depend on my recent experiences with the ship more than anything. I'd probably consider Nein Nunb a must if I were sticking it on a YT-1300 to give myself as much maneuverability as possible when trying to shake that stress token too. Which if you're going there, you might as well give Lando a pretty hard look as he's throwing around Focuses when he does green maneuvers, which he'll have more to choose from with Nunb as Crew, bleeding off stress tokens."