I suspect that even if they close the training program, things would be setup such that current trainees should still obtain all standard training (e.g., didactics), potentially with minor modifications, depending on the nature of what's happening. Especially at VA, it'd be highly unlikely that they'd just close the program outright while current trainees are still there. Although a hiatus on taking new trainees also doesn't definitively mean they're closing the program. That's one very real possibility, but not the only explanation.
When/if they do close, they'll probably have someone designated to be the point of contact for future training-related matters, such as verifying training completion. Still, I'd plan to get your supervisor(s) and/or TD to fill out any necessary paperwork as close to the end of training as possible. I'd also then scan and backup that paperwork and your completion certificate and save a few copies (e.g., with yourself, possibly in cloud storage, and possibly in a credential banking service), just in case.