Google's Hangouts service has the neat ability to easily turn logging off so you can safely talk without having a record of your conversation. However, if you ever opened a picture in its own tab, you can probably find it in your browser's history by searching for "googleusercontent".
On the desktop, when you click on a Hangouts picture message, it opens a new Google+ tab displaying your image in an album. If you have logging disabled, this picture will disappear from your Hangouts album in a day or two, and you won't be able to find it anymore.
However, if you right-click this picture and choose "Open image in new tab", your browser will save this link (assuming you have browser history enabled). You can find this link later by searching for "googleusercontent" in your browser's history. Your Hangouts history and photo album may not report the "deleted" picture, but the direct link to it still works (in our tests we were able to find pictures at least five months old that were no longer accessible via typical Hangouts history hosted on Google's servers).
This isn't exactly earth-shattering news, of course. You should assume that your recipient can save your pictures no matter what, whether you're sending them via off-the-record Hangouts or Snapchat. However, if you're on the receiving end of some adult-themed content that you don't want logged, don't open the picture in its own tab. And, if you do need to find a picture that you meant to save but didn't, this search might help you out.