Candidacy does not refer to persons: it is a status attributed to persons, the fact or manner of being candidates, not the candidates themselves.
Thus, one may say that “X announced her candidacy”, meaning that she has assumed the status and undertaken the role of candidate for an office. When the newspapers discuss her candidacy they are not talking about the candidate herself but about such matters as the manner in which her campaign is run and her likelihood of achieving the office for which she is campaigning.
Likewise, candidacy does not refer to the office for which one is a candidate: it is the status of being considered or considerable for the position.
Accordingly, in announcing an opening it is not referred to as a candidacy: that is the status of the persons who apply for the opening. The institution does not advertise a candidacy, but a vacancy or position or appointment or some such thing, and it does not seek candidacy, it seeks candidates.
In some cases, candidacy is officially defined. For instance, in many universities a graduate student who has satisfactorily completed a required curriculum (and the required paperwork!) is formally admitted to candidacy for an advanced degree. This doesn't mean that the student has earned the degree, only that she is now regarded as worthy of being considered for the degree and is now admitted to the advanced studies in which she may actually earn the degree.
So in advertisements for academic positions you will sometimes see things like “Doctorate or candidacy required”, meaning that only persons who have achieved at least candidacy for the doctoral degree will be considered for the appointment.