Thank you for your patience as I prepared my response.
So unfortunately when one tries to help a friend/relative out by allowing them to stay at their home for no/low cost, if the arrangement is long term (generally defined as longer than 30 days) the court will consider them a tenant at will. What this means is that they are no longer simply a guest, but rather have the same rights as a tenant, which requires the owner of the home to go through the legal process (ie providing formal notice to vacate and following through with the legal eviction process if they fail to vacate).
OH does not have any requirement that a lease be in writing. So if there is an oral agreement that one will contribute to the expenses of the home, then the owner may sue for those damages. But in the meantime, in order to remove the tenant at will the landlord would need to follow proper legal procedure.
If there is an executor (if the house is still in probate) the executor would be responsible for handling the issue, as the executor is responsible for maintaining and preserving the estate assets.
If there is no written or oral lease that specifies a time frame, generally the courts will construe the arrangement as a 30 day tenancy (for this, please see section 5321.17 located here: http://codes.ohio.gov/orc/5321)
For information on the eviction process please see:
Many times, a tenant can be paid to leave- basically to avoid the legal costs (and hassle) of a formal eviction. The landlord will often offer the tenant money to vacate by a certain date and turn over the keys. Others prefer to go through with the formal eviction process, and then seek damages from the tenant.