Indeed; while I've not had this specific issue with the phones, I do still have a mid-2013 MacBook Air lying around (it's now too old to realistically sell), and the battery on that was so worn by the time I got an M-something to replace it that would go from "fine" to "emergency shutdown" during boot if I forgot to plug it in. And then report something like 20% if I plugged it in and immediately booted it again.
