It seems like Carter in Person of Interest really is dead.
Actress Taraji P Henson, who plays Carter, commented that actually killing off the character was a great thing for TV.
She explained that the writers' decision to go down this route was refreshing, because too many shows are afraid to take that realistic approach.
In real life, bad things happen - often to people who don't deserve it, and if Carter lived on - it would be "too neat and tidy", too much of a happy ending.
Here's a quote from the interview Henson did to clear things up:
"I just want them to know that this was always going to be Carter’s story. She was never meant to last forever. And art imitates life, and sometimes the good guys don’t make it. Sometimes they’re the ones that lose in the end. I think what we did for TV [on Tuesday] night was great. I mean, TV needed that. So many times when you watch these procedurals, by the end of the show they found that one little piece of hair in the big old carpet that solves the whole mystery. Life is not that sewed up in the end. No, it’s messy and it’s ugly. Just when you got your life together is when you walk outside and catch a bullet. That’s life."