You might have problems if it was all verbal. I'm sure you don't need telling but you should get everything like this in writing.
The first thing I'd check is who is listed as being the administrative, technical contacts and the Registrar for the domain, if it's the new company the old one can't "cut you off" if it's the old company then they can take the domain over and effectively cut the web site off.
the easy way to do that would probably be to contact the new hosting company and explain the situation to them and your concerns about being cut off as they will know instantly what to check and will be able to decipher the results a lot quicker and easier than them being explained on here.