If you disjoin them from the domain first (which you don't have to, as mentioned by MDMarra), the user profile will not be affected - it doesn't get deleted. Of course, it will be inaccessible to normal users, and the old domain user won't be able to log onto it, so you'd normally copy all the documents and settings out to a local user's profile first.
And while it's possible to let these machines used cached credentials indefinitely, it's not a good idea. Much better to setup a simple VPN and have the users VPN in, which you can do fairly easily on a Windows server with an external IP address. See this Microsoft support KB for how to do so, because, again, this is really the much, much better approach than having them orphaned from the corporate network, whether they're domain-joined or not.