Can you no longer have any sites hosted by them or just the one shut down? Do you just go to another hosting company or is your domain screwed too?
That's why you always have to have backup of all files. You will waist some time uploading, but you are safe.
It is a good idea to check the availability of your site once in a while because you don't know when the server will be down. The moment the server shuts down, look for an alternative immediately. Otherwise, you will lose your potential customers / visitors.
Switch to a new host with your backup files which hopefully you would have. Otherwise it'll be a lot of painful work to recover everything you might've lost...
Just ensure two things (1) You have control over your domain (2) Backup regularly and you will be safe and not at the mercy of any hosting companies.