No and it's not possible. It would mean that no one was seeking to gain or change employment and no one was seeking to hire or fire. In essence, it would mean a static situation without growth or change in the labor market; given that population tends to increase and people tend to shifts in various demographic characteristics (age, marital status, etc.), a static labor market would be necessarily underserving any society.
This is a repost from my replies to questions posted on Quora, a question-and-answer site where questions are asked, answered, edited and organized by its community of users, at quora.com. The questions and their subtexts are not mine.