Thanks for explaining!
Just to sketch an example to determine if I get this right
My girl plays Targaryen and she has the Rhaegal card in play. For whatever reason he dies and gets put into the dead pile. When she draws new cards and Rhaegal comes along the second time she cannot put it into play because the first card has already been killed?
That's exactly right.
Rhaegal in the core set has the ability to search the deck for another copy of himself and attach it as a duplicate.
If you starting to add cards to the decks you already have you will often find that this is the dangerous issue with unique characters.