I haven't tried Exile survivor yet, so take my opinion with a grain of salt: I might be full of it and I'll edit this review if I change my mind
This card is hot garbage
Permanents that grant you exp or exp discounts are better bought at the start of a campaign: this usually does not actually come up because most cards that grant you that bonus usually MUST be added at the start (with a price attached to them): In the Thick of It, Arcane Studies, Down the Rabbit Hole. The only excpetions that I can think about is Charon's Obol, which can be bought whenever you have 2 exp to spare and Observed for 4 exp sometimes can grant you free exp; still, to get the most of these cards you must buy them as soon as you complete your first scenario if you can spare the exp
That means, you have to have 5 exp ready after you immediately complete the first level of a campaign to use Déjà Vu: I think it is possible to accumulate enough exp in every starting scenario of any campaign to purchase it, but the price is not cheap, that likely means you will not have enough exp to actually buy anything else but 1 or 2 cards. If you actually do not get enough exp to buy Deja Vu, you either must save what you got until you complete the next scenario (and get NO CARDS beside any story asset you won) or give up and just spend the exp on something else and forget about this permanent
But that's not the only problem Deja Vu has: like the high exp cost already is a deal breaker but it gets worse.
Almost every exile card (which is different from "remove from the game") is above level 0, which means it needs exp to be added to your deck, exp you just burnt buying this bloody cat
That means not only you spend A LOT of exp for something you cannot properly use until you get enough exp to actually buy some damn cards that exile, but it also means it takes forever for Deja Vu to actually pay itself in, because the exp discount does not stack, you cannot reduce the cost in exp of any card above level one further, like A Test of Will, Fire Extinguisher, Fortune or Fate, Stroke of Luck and Unscrupulous Loan (if you are unlucky to lose it). You would need to rebuy up to 3 exile cards between 3 scenarios to finally break even and reap some benefits!
Thankfully the majority of exile cards ARE level 1, so they are relatively cheap, but it does make harder to keep any card above that cost given you may have to also pay an 1 or 2 exp of your own pocket
But we are not done yet ladies and gentleman, because there is one obvious cavet that essentially leaves this card dead in the water.
It only works if a card gets exiled, of course, but sometimes you don't want or need to exile a card:
-You may just not get damage or horrified enough to lose Leather Coat or Cherished Keepsake.
-You may not find an ally with Flare
-You may not need to use Stroke of Luck effect to actually pass a skill check
-You may always pass the test of the level 2 version of A Test of Will to not need to rebuy it (or you may never need to use the level 1 version)
-You may never need to cancel that much damage or horror with Devil's Luck
-You may not take enough horror to lose Guiding Spirit
-You may not need to prevent doom with Fortune or Fate
-You may not need to use Burn After Reading (even though you DEFINETLY should use it if you purchased Deja Vu, because it synergises so well with it giving you another target for the exp discount)
-You may not need to use the exile effect of either Fire Extinguisher
-You may not have failed enough skill checks to justify using Lifeline or don't need the extra actions anyway
-You HOPEFULLY won't lose Unscrupulous Loan
Keep in mind, it's more likely for something to be exiled the more cards you put in your deck that can get exiled, but those cost exp you just spent for this guy who scratched your sofa and pissed in the living room
There is a reason why Charon's Obol is considered a staple for most rogue decks: I do not agree because the unpredictability of the campaign might catch you off guard and cause you to lose all your deck progress in one fell swop, but on a replay, once you know what the game is gonna throw at you, it's without a doubt one of the strongest cards in the game. Just pay itself out in the time frame of one scenario and scales so well. Sure unlike the Obol, you can stack Deja Vu twice, but that would be one of the biggest meme decks I ever seen to spend a total of 10 exp on permanents that do nothing until you get 6 more or so
About the only good thing I can say about this card, is that the visual joke with Stray Cat is actually quite subtle and clever