Legal Question in Landlord & Tenant Law in Missouri

Re: Ownership of discovered property on rental

It belongs to whomever buried it, even if that was a prior landowner.

As a practical matter, it will be difficult to prove who buried it, so the likely answer is that it belongs to the landowner, not the tenant. The tenant occupies the space, the landlord owns it, and hence, has the rights to anything found thereon that cannot be shown to belong to some third party. If you were to accidentally find oil on the property, the oil would not belong to you. It would belong to the owner because he has not relinquished those rights to you. Since he retains ownership, and has not leased any right in the land other than occupancy, the artifact belongs to the landlord.