Handle the "transition" process (during which the student is still officially on the payroll)?
Support would be great.
On the other hand:
If you are talking about a PhD student who was employed at an institute, then maybe the advisor should think what he/she has made wrong concerning advising.
From my point of view, a retrospective would be worth for both - student and advisor. For instance, can you remember the first time when an expectation and an actual state of the student's work was rather different. Talked the advisor with the student regarding publications and interesting conferences? Which intervals were scheduled for meetings? Did their meetings worked out? If not, why not? (agenda, interruptions during the meeting). Which method was used by the student to assess his/her progress? Were these "story points" observed a little bit by the advisor?
Discuss the situation with the group, to maintain morale?
Yes, but firstly the advisor needs to know the actual reason concerning the end of the student's work. Talking in front of a group about a reason which was not the actual reason could be not the best when having persons in the group who are friends of the student who ends his study and work.
Help the candidate, should she wish to apply elsewhere?
If she has achieved a certain level within her scientific field, why not?