We’ve heard frightening stories of people who have been hit by huge bills because of annoying marketing calls that went to voicemail, so that's something you really need to avoid, such as this article in the Telegraph.
For those with voicemail greetings that get changed about as often as a new president is elected, know that this is doing a serious disservice to the caller-recipient relationship. It signals to callers that the business is anything but an authority, most likely not very detail oriented, and has questionable overall credibility and competency. Those aren’t traits that any business wants to associate itself.

Increase the odds of getting a call back by mentally composing your message before each call. And remember, people hate it when callers state their name and phone number too quickly in voice mail messages – no one wants to listen to a message ten times to comprehend simple information.
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.