Oh - if anyone is still curious: I recorded the greeting via the phones custom greeting function, then called to listen to it from another phone, then turned off the phone and called again. Same message. I had wondered if just maybe the phone played the message when on, and the carrier played the message when the phone was unreachable.
41 Funniest Voicemail Greetings in the World. Many years ago, in a time before cell phones (Yes it exists, and I remember it!) I used to get inundated with phone calls to my landline at all times of day and night.

Hi Mary! First of all, I’m so sorry to hear that. What a horrible thing to have happen! It really depends on the manufacturer. There are high quality picture frames and small, less expensive ones that probably don’t have a lot of memory or ways to protect what’s been recorded. I would start with the manufacturer to see if they have any ideas. If they can’t help, try one of the recording suggestions we made in the post to see if they might be able to help. Even some Walgreens and Walmart have recording services, that preserve recordings, so they might also be able to help.
Yes, it will dial the voice mail but then the recorded voice gives you various options.