O3 with Departing Team Member

O3's - Yes - employees get O3's - Yes.

Couple questions, though, that would negate the need for the question:

Is the person meant to continue productive work for the next month?  You should expect and support them as their focus will be elsewhere.  I would prefer to let the person stop showing up to work at all - even if he or she will get paid for not showing up - if possible.  

Is this layoff public knowledge?  If so, you should allow the person to avoid the shame of seeing people (coworkers) who will be in a state of awkwardness around the employee being let go.  If not, you need to be careful not to allow the water cooler assumption of more "restructured layoffs" to come in the next month (assuming, of course, there are no further layoffs expected).  

I recommend continuing O3s. Two reasons: First, your direct is still working and delivering work product. Second, as the supervisor, you are in a position to both provide referrals and be a reference for your direct after they leave.

You do not indicate anything about the quality of your relationship. However, let me add that I have had a direct in an identical situation--though there was increased tension at the beginning of the "wind down"--I was in a position to be a reference after their departure. We remain in touch even years later.

I would definitely continue the O3's - if nothing else, focus on career development / management. Maybe offer to do mock interview, discuss opportunities s/he is looking into, maybe resume review. This, of course, is in addition to the phase-out process - status updates, hand-offs, transfer of knowledge and so forth that needs to occur prior to their departure.