The domain name registrant (the person who legally has control of your domain name, which should be YOU) can do anything they want with it, so if your email accounts are not protected or you fail to renew your domain name, it can be stolen or registered by someone else. This is different from a web designer holding your domain name hostage though.
When a scammer holds your domain name hostage, they request a ransom (usually thousands of dollars) to transfer it back to you. You might think this is something you would never entertain until you visit your website one day and see that it's gone, and the website address you've had on your business cards, signs and trucks for years no longer works. Or even worse, you visit your website and see that it's been forwarded to a Canadian pharmacy website, or even a hardcore porn site, the latter of which can put you out of business!
Protect your logins and passwords to your domain name account, as well as any email accounts associated with your domain. If your email account is compromised, the thief can find the emails containing your domain name account login and password, and transfer ownership of your domain name.
Most importantly, never forget to renew your domain name. The domain registrar (GoDaddy, etc.) always sends multiple emails weeks and days before your domain name is scheduled to renew. The domain name will renew automatically if the credit card on file is correct (although some bargain domain registrars may not automatically renew the domain, which is why it's important to go with a well-known domain registrar). But if your credit card has changed or expired, the renewal will not go through and you'll lose the domain name. Sometimes scammers will buy the now-expired domain name and forward it to a porn site, or something else that you wouldn't want potential customers to associate with your company. Then they will email you for a ransom to get it back. The chances of getting the domain name back if you pay their ransom or attempt to take legal action is highly unlikely. If something like this happens, your only recourse may be to change your company name. That's how serious this is! However, if your domain name did NOT expire and they simply stole it, you may be able to get it back with help from the domain registrar.
If you close your business and take down the website, you may still want to continue renewing the domain name for a few years (it's only something like $30 a year), so as not to bring down the reputation of your old company by having a scammer grab it and forward it to a porn site!