Here is my understanding,
ACGME approved fellowships are PGY-V years by definition. These include sleep, CL, forensic, geri, addiction… If your fellowship ends in an NBPN examination, as it currently stands, you must complete a PGY-IV year to be eligible for this training. You just cannot be a PGY-V after a PGY-III year.
If your fellowship isn’t accredited, there is not examination and they give you a nice piece of paper and you get to put it on your CV. Some of these are called Community fellowships, emergency psychiatry fellowships, mood disorder fellowships. I suppose this can be a PGY-IV year, but your new program would have to graduate you from general adult training and have a general adult program to do this. You would have to be under the training of the general adult PD, not the PD of the fellowship. Non-ACGME approved fellowships cannot give you ACGME training credit. This would be a transfer to a new adult program, or if the same program, it would be essentially hanging out with the fellows for your elective time. The issue at hand is if you truly completed a fellowship or not. This would be completely at the whim of the fellowship director. Unaccredited fellowships can hand out parchment to anyone as there are no real rules. There are a lot of rules about what would count for an ACGME PGY-IV year. Do these fellowships have 360 evaluations, do they monitor duty hours, and do they require participation in QA and QI activities?
I guess there might be some politics over who funds the PGY-IV (pseudo PGY-V) position as far as whose budget it comes from. At our institution, you cannot be paid as a PGY-V before you have completed a PGY-IV year.
Please be wary of the other ACGME rules like, 2 years must be in the same program, and there must be at least 12 continuous months outpatient. Too much moving around can make you not board eligible even after 4 years of training.
As others have pointed out, there is talk about changing this, but so far I believe this is the way it is.
This is my idiosyncratic interpretation of the question at hand. I could be wrong, but please be careful when playing around with training. The ACGME and the NBPN are not very flexible as it is their job to insure the quality of training.