The classic case is the underproductive but friendly and intelligent person who has a good rapport with everyone in the office, good answers/comments in discussions with coworkers, willingness to do miscellaneous odd jobs and help people out, etc.
In that case, I'd question if that person is truly unproductive. More likely management just doesn't understand how to properly value their actual role, which may not be reflected by their job title. In that case, instead of firing them, it might be better to either:
A. understand the actual value they deliver and leave well enough alone
or
B. create a new title for them, which reflects the value they produce and then hire somebody else for their old position.
In that case, I'd question if that person is truly unproductive. More likely management just doesn't understand how to properly value their actual role, which may not be reflected by their job title. In that case, instead of firing them, it might be better to either:
A. understand the actual value they deliver and leave well enough alone
or
B. create a new title for them, which reflects the value they produce and then hire somebody else for their old position.