It is possible to wind up with a character that is both in play and in the dead pile. This has no effect on the character currently in play; there is nothing in the rules that prevents this situation. The rules on dead piles/uniques are quite explicit; having a copy in play simply prevents you from playing/putting into play/taking control of further copies. This does have the following practical application: you can no longer place a duplicate on your living copy of the card, as marshalling/putting into play a copy of the card is prevented by the presence of a copy in your dead pile.
House Lannister. Non-Loyal.
Character. Cost: 7. STR: 10.
House Clegane. Knight. Lord.
Reaction: After Ser Gregor Clegane discards a character using pillage, place that card in its owner's dead pile. Then, you may choose and kill a character with printed cost equal to that card's printed cost.
The King's Peace #49.
When this guy came out, I was scared. The 10 STR is almost a guaranteed win during military challenges—and that reaction—yikes. Unfortunately, The Mountain takes too big of a hit with an Imprisoned, Nymeria, or a Milk.