If you are hosting you should be doing backups - that way if this happens you can move your files elsewhere.
As for domain names, if you purchase that from the host you should be able to get them back but it won't be easy and you will need proof (purchase emails etc).
The biggest thing is find a decent host and don't just base that decision on price. The price you pay depends on the importance of your sites. Overall, backups, backups, backups - don't depend on anyone but yourself for backups and make sure they are kept away from your current host!