They do - but as she gets older, unfortunately so does my mother.
Long shot here, but is there any chance she has any kind of voice-to-text feature enabled, and she’s muttering a possible reply?
I used VTT heavily a few years back when I had wrist surgery. Sent a friend a message while I was in the recovery room with my husband after he had surgery. And the phone decided I was still talking afterward. It didn’t actually SEND the rather bizarre text, but it definitely tried to transcribe what it heard.
Otherwise, I agree that it sounds like a particularly annoying (and useless) chatbot.
I realize that I didn’t check her iPad, which has iMessage on it, and her messages usually are tagged with her Apple ID (RoboMIL@icloud.com) rather than her Contacts name. I bet it’s in there. I’ll check tonight.
I"m glad you are going to check tonight.