I was researching a relative in Champaign County, Illinois. A vertical file on the family contained a death notice from an undated, unsourced newspaper that indicated the relative was killed by a train.
The only problem was that the newspaper clipping was a photocopy of the original. There was no reverse side I could look at for clues. There was just the clipping. I was concerned I would have a difficult time locating the person with just a clue that he died in Indiana.
Then I remembered the deceased had an interest in an estate in the county where he lived. Researching court and probate records located a file settling up his estate. Included in those court records was a transcription of the coroner's report from the Indiana county where he died. Problem solved without looking in one Indiana county after another.
You can't solve every problem this way, but exhausting all sources where you know the person had been may give you clues to help you pinpoint those other areas.