In a recent episode of the Fox sci-fi drama, the Observer (Michael Cerveris) predicted that Olivia would die.
"We ourselves get frustrated with other shows that only ask questions and leave things up in the air and don't really answer them," Wyman told TVLine.
"We really take pride in saying, 'Look, our drama is strong enough that we can actually answer the questions'. Let's just say that we're going to try to get you satisfying conclusions for all those things that are up in the air."
Olivia's death was first foreshadowed in 2011 episode 'Lysergic Acid Diethylamide' - the instalment suggested that a mysterious figure in a zeppelin (Ulrich Thomsen) would ultimately kill the government agent.
"You'll learn a lot more about the Observers this year," said Wyman. "And yes, you probably will understand a lot about that guy in the zeppelin."
Fox chief Kevin Reilly recently revealed that Fringe is losing money for the network on Friday nights, casting doubt on the show's future.
Series star Joshua Jackson (Peter Bishop) has since indicated that the series could continue on cable if it is axed.
Fringe continues tonight (January 27) at 9/8c on Fox. The show returns to Sky1 in the UK in February.
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Watch a preview for the next episode of Fringe below: