What do you do when a lease runs out on a business and the people refuse to sign a new one.

Once the two-year lease ran out and they refuse to sign a new lease, they revert to a month-to-month tenancy if they are still in possession of the property. This means that their tenancy lasts for one month at a time. Either you or your lawyer could send them monthly invoices for rent which would hold up in court. If the case went to court and you tried to collect on the back rent, the judge or magistrate would be interested in knowing whether they continued in possession after the lease was up and whether they paid you any rent. If the rental invoices were reasonable in amount, which still could be higher than the lease rental, the judge or magistrate should give you judgment for the rent arrearage. I understand that you don't want to evict them, but as a landlord you have a duty to advise them of the stated rental, and if you don't send them invoices putting them on notice as to what you are charging for rent, then you will have a difficult time later on in court if you have to sue them for the back rents.