The only way to avoid that is to prevent hotlinking, a bad practice in forums, blogs, etc. Notice your readers not to hotlink images from other sites, I think is the best thing to do.
Hotlinking is NEVER acceptable behavior unless it’s from a site that promotes it (like imageshack.us) as something they provide.
Unless you want to figure out a way to have your forum dissallow links TO the image site, the best thing to do is make a post now to tell people not to hotlink. And when they do it, edit the post to remove the image and tell them ‘Hotlinking is BAD AND WRONG.’
http://altlab.com/hotlinking.html
OK. After doing more reading I agree that hotlinking is bad practice.
However, we get 2500 posts a day on the forum, moderating all this is an impossible task. We have a team of about 10, but lots of images do get through.
I was hoping there would a technical fix.
We are now considering a blacklist – which would be impossibly long, or a whitelist – which wouldn’t cover all acceptable places, especially personal web hosting accounts.
Offer hosting for the images for your members so you stop them from hotlinking.
https://bbpress.org/plugins/topic/bb-attachments/
while that is an option I think we’d have many copyright issues to deal with…
Turn off inline images and allow links only.
There’s no way I know of on any forum to stop morons from hotlinking.
There aren’t any system to prevent users to hotlink images. I’ve managed a forum with more than 50 thousands unique visitors per day and in that situations is absolutely imposible. The only way is to have a lot of moderators
I didn’t try it but perhaps with htaccess you could allow images only from some image servers like imageshack.us or flirk
I agree, hot linking is not acceptable. Just imagine that you a re the hot linked one and a post with your hot linked images goes to digg number 1.
we have thought about a whitelist of acceptable places to link from.
But this would cause issues with peoples own hosting accounts, and also linking to images from manufacturers who would want their images linked on forums. It is a cycling site and many discussions revolve around new bikes – it would be a huge list.
I think the best bet would be to block the inappropriate ones. 
Add to .htaccess
RewriteEngine On
RewriteCond %{HTTP_REFERER} ^http://(.+.)?crazy-porn-site.com/ [NC,OR]
A blacklist is also an option but our problem is not stemming from blatant porn sites, but rather image replacements used on perfectly acceptable sites.
This would then only work through adding the sites as their hotlinking intentions were realised by a nasty image appearing – the damage then already being done.
There’s no easy answer!
> rather image replacements used on perfectly acceptable sites
I would say any perfectly acceptable site, which is OK with hotlinking, would NEVER do this. If you’re using their site against their terms of use (i.e. no hotlinking allowed) then they’re within their rights to serve whatever image they feel like.
I think if I had this problem I would tell my users that images will only be displayed from a whitelist of image hosting companies; no other companies will be allowed. Then, whitelist that site only. If it’s a perfectly acceptable/reputable site, which allows hotlinking, then they will never replace the image and serve something else. Of course, your users should not be hotlinking in the first place, and because you allow it, you have this problem. Allowing uploads to your server with the bb attachment plugin eliminates the issue of images being replaced and displayed to your members. You mentioned copyright issues: well, if your members don’t have the right to use the image in the first place, they shouldn’t be loading it onto an image hosting service anyway: the copyright problem exists there as well.
I suspect you could start out with a small whitelist or blacklist and see 80% of the problem go away very quickly. There’s probably a “good enough” solution. Do something, don’t overthink it.
My 2¢
Disable the IMG tag and only allow bb-attachments for images.
You’re lucky the remote site isn’t replacing the hotlinked image with something illegal which would get your site shut down by your host and/or law-enforcement.
