You have a Facebook page for your business!
The way Facebook works is that the business pages are connected to the person who created it. So if you got someone to make you a facebook page for your business, that Facebook page is linked to their account, it is their property. Now say they leave your business, there can be problems as even if the person gives you admin access to that page, as it is still technically connected to and owned by them. In today's case, the separation has not been a happy one, and they refuse to even talk to the owner of the business.
The only way around this if they wish to continue with Facebook is to start a new page and start again. They then have to report to Facebook that the old one is impersonating the business which is messy as I am sure that Facebook does not want to get involved in disputes regarding the admin position of this page.
If you have such a Facebook page now, make sure that it is linked to your account. Also, consider giving someone else your passwords just in case something happens to you, and so the business can still use its Facebook page. If you are reluctant for some reason to do this, consider setting up a “legacy contract” for that someone who will take over an account is for some reason you cannot.