FlipperVolt only deals with data about images, and does not store any images. If a Tumblr or Reddit (etc.) site is removed, then images from that site will no longer be viewable through FlipperVolt, even if you mark those photos as a favorite. But you do have the option to save any image to your desktop. It is advised that if you like an image, you save it to your desktop and not rely on it continuing to be available indefinitely.
If you change the download “Save Action” option in the settings page, you can opt to download-and-hide, download-and-favorite, or download-and-do-nothing when the “J” key is pressed or the floppy-disk icon is clicked.