Thanks Palcouk.
I did wonder whether going into hibernation might draw more power than the battery could able to provide if it is already low, but that would depend on how the low battery threshold is set.
The alternatives would be immediate shutdown or going to sleep, and sleep mode still draws a little bit of power. I'd prefer sleeping to abruptly turning off with no warning.
The battery health is fine, BTW. I get pretty much the full expected run time I have always gotten since it was new.
Really, my biggest concern is the lack of warning. A decent warning would let me handle it, by plugging in or whatever.