Domain Names, are the sign post that directs the internet to find the server your website is installed on, this is called a Domain Name Sever Address or DNS
If you did not register the Domain Name yourself , then you may not have a domain register account, in other words if you can’t login to a website and have your details and billing account available to you then you almost can say you have no control over your Domain Name.
Any changes to a Domain Name is always confirmed by an email, if it is not yours then no changes can be made.
The Domain Name has 4 different contacts: Registrant, Admin, Tech & Billing unless you have all of these in your name with your email address, you could be in trouble unless you can contact the company that the Domain Name was purchased through if they are contactable. (Most only use email and will only talk to the Admin contact)
All DNS updates or changes are requested by the Tech Contact, once it has confirmed by email that the request has been made then the change will occur, no response means nothing changes.
What does all this mean, simply if you cannot control your Domain Name, you have no control over your website, if the website host no longer operates or decides to increase hosting costs you are screwed.