The thumbnail nobody thinks about
Cameras write a small preview into the file so gallery apps can show it instantly without decoding the full image. It lives in a second directory of the EXIF block. Some editors update it when you crop. Plenty do not, and simply leave the old one in place.
This has gone wrong publicly, more than once
The pattern is always the same: someone crops a screenshot or photo to hide a detail, publishes it, and the embedded preview still contains the uncropped frame. It is recoverable by anyone who opens the file with a tool that reads EXIF, which is to say, anyone who cares to look.
Redaction by drawing over it is a separate trap
Pixelation is the risky one: where the hidden content is text in a known font, researchers have reconstructed it by searching for the rendering that pixelates to the same blocks. A heavy blur on a photograph is far harder to undo and often practically safe. Solid black is safer still, but only if the image is then flattened and re-exported — in a layered file or a PDF, the covered content usually still sits underneath, fully intact.
How to be sure
Drop the file in above. If a preview is stored inside, this page will render it on screen so you can see exactly what a recipient could recover. Cleaning removes it along with everything else.