At 84 with multiple underlying health conditions and problems eating, I wouldn't overly worry about an hba1c of 51.
There are two reasons to be worried about high BG. The first is symptoms affecting quality of life (recurring thrush, thirst, waking up to wee multiple times a night etc.) Not an issue she likely has with her hba1c only just over the diabetes threshold.
The second is complications from many years of high BG. Her numbers aren't very high from a diabetes point of view, and while I wish her many more happy years, it isn't that likely she'll live to a 110 to give her time to develop complications with slightly raised numbers.
If a family member of mine would be in this situation and struggling to eat, I'd be happy for them to eat whatever takes their fancy to sustain them.
Do you have a medication list? Is she on steroids like prednison or dexamethason perhaps? This would explain the sudden jump in hba1c.