Do they have to repeat the year and graduate a year later?
In short, no. Typically a program closes at the end of an academic year so you’d just move and start your next year at a new place or something similar. There is a longer answer to that, of course.
When a program typically closes it is known months ahead of time and follows at least 1 or more years of ACGME warnings. Unless your program has been so bad you haven’t been getting “reasonable” training you get to continue on. You have to apply to other programs and waivers are given to them allowing them to have a temporary increase in residents - plus, your funding follows you so the new institution gets essentially more residents for free. Hopefully you get to move somewhere close, but in some cases you have to move to an entirely new state. This was a HUGE issue when Hahnemann closed this year in Philly, and still somewhat unresolved - but that’s an institutional closure.
If there was no ACGME action on Largo (you can look it up), then they voluntarily closed. Maybe they weren’t going to meet permanent accreditation standards as I believe they were a new program (you see this more with rural, new FM programs that end up not being able to support a training program with any depth). Or they just decided it wasn’t worth it.
VERY rarely the ACGME revokes accreditation without the long warning and probation process - the only instance I know of is in Ohio when the EM physicians were replaced with an entirely new group by surprise overnight (this happens more with EM, where corporatization is much worse than in our field). Since none of the academic faculty were left, the program had to shut and the residents had to scramble. Look up Summa EM residency for more.
I saw this orphan process first-hand when a community surgery program was closed in Daytona Beach - the residents moved in July 1 to new places and they somewhat lucked out because they went to higher level academic programs at UF, Miami and Emory. The downside is all had to move mid-training and uproot families.