It goes down with the instance. In case of posts, there’s only a very low resolution cache kept. Images are not federated, just links to them.

Theoretically you could do overly compressed JPEGs in base64 as data: URI or just other tiny images like I’ve did in this comment for demonstration, but this is stupid.

I’d recommend just using Imgur or similar.

Edit: Here’s an example post with image hosted on dead instance: https://lemmy.sdf.org/post/278052
It’s gone. Reduced to atoms.