I have run servers from my home before, LONG ago...but it really doesn't take much, aside from bandwidth issues on a media heavy site. A daily backup could be FTPed to a backup server to keep things as current as possible...and saved should our hosts decide that the party is over. A less dynamic site like the Weebly guide site should, and probably is already saved on the admin's machines anyway.
After being threatened by the RIAA over my KISS bootleg video tape site back in 99....I was constantly worried about having my hosting removed and data deleted, so I just kept my home server synced with my live site, so if anything happened...all I would have to do is point my DNS to my home server and it could limp along until friendlier hosting could be arranged.
It might be a good time to brush up on using TOR.