Can't transfer web pages to new host

I owned a URL and had it hosted by a small company; well and good, but they stopped trading. They gave me plenty of notice and I attempted to transfer the URL (with some others I own) to a new hosting company. All but one worked fine.

The original company are now not responding to 'phone and email and my URL still points to their machine, which may be decommissioned at any time. The new company can't simply take the URL (obviously, or URLs would be stolen all the time). What action should I now take?

I would contact a new webhost and talk to them in person,
explaining what happened. They might know how to go
about dealing with this through the registrar. I'm sure others
have gone through the same thing.

The alternative would be to wait until the domain name
expires and register it again.

Did you purchase the domain or did the people you originally used for hosting purchase it for you?

Did you purchase the domain or did the people you originally used for hosting purchase it for you? They registered it, hosted it and supplied me with the ftp commands to update the pages.