Ohio law does not require that the landlord change locks between tenants, nor does it require that the landlord pay for the locks to be changed after a burglary. The lease may contain a relevant provision, but odds are that if the lease addresses locks it's to the effect that the locks may only be changed with the landlord's permission.

If the tenants can prove that access was made with a key, they might be able to convince a court to order the landlord to cover the cost of changing the locks -- but that would require litigation, and would also require the court to conclude that the key used was not a copy made by the tenants. The court might also conclude that it was possible that the tenants forgot to lock their door. Absent something in the lease that would require the locks to be changed, it would be a tough case to make, and would also likely cause the landlord to decline to renew the tenants' rental at the end of their current lease term (or give notice, if they're month-to-month).