Jim and Becky took their grandparents to the airport where they let out a sigh of relief.
He doesn't do it as often, but Jake and Elmer still like to go fishing on Saturdays.
The sentences above are vague because the pronouns "they" and "he" do not make it clear to whom they are referring. In the first sentence, who let out a sigh of relief, Jim and Becky or the grandparents? In the second sentence, who doesn't do it as often, Jake or Elmer?
The sentences may be rewritten to correct such ambiguity, as is shown in the following instances:
Jim and Becky took their grandparents to the airport, where the former ones let out a sigh of relief.
Jake doesn't do it as often, but he and Elmer still like to go fishing on Saturdays.