Let's say I have a Karn, Scion of Urza. I tick up, and one card gets exiled with a silver counter. Later, that card is processed by Wasteland Strangler, reanimated by Reanimate, and then re-exiled by Swords to Plowshares.
Can I now tick down Karn to add that card to my hand? That is, after all these interactions, does that card still have a silver counter? If not, at what point does the card lose the silver counter?
What if the card that's exiled is Eternal Scourge, and I choose to cast it from exile - does the Eternal Scourge enter the battlefield with a silver counter?