Everyone has previously given a good answer. As a landlord I have had the opportunity to be in court in front of Commissioner Singer for evictions. During this time I was privileged to watch Commissioner Singer deal harshly with someone in similar circumstances who was making excuses as to why they did not pay or have the money to deposit with the court in order to pay the lawful owner.
The Victorville Superior Court is not friendly to those who try to avoid lawful payment to the owner. While the following is not legal advice, my experience has been that if you make a reasonable effort to pay, by sending the check or money order to it's normal place (there should be a place in your rental agreement for legal contact or service on the landlord) then you can avoid any problems in the future. Just keep copies in a safe place--like with your rental agreement.
The landlord may have had a will. If he did, he may have specified who would receive the home.
If the landlord and his spouse owned the home as tenants in the entirety (husband and wife), the spouse becomes the owner. If the landlord and someone else owned the property as joint tenants, the other owners remain the owners of the property.
If the landlord held the property in an LLC, the LLC remains the owner of the property.
If the landlord held the property in a land trust, the trustee of the land trust was and remains the owner of the trust. The question, then, is who has power of direction over the trustee.
In other forms of trusts, there's usually provision as to who becomes the owner.
So, there's no simple answer.
It's likely that someone (most likely the landlord's spouse or a child) will contact you regarding future payments. You should, however, verify that the instructions are correct--that the person who says "Pay me" is actually the owner of the property or is the one designated to receive payment.
If no one contacts you, contact a lawyer. He or she may direct you to deposit your monthly rent checks into an escrow account (that he'll set up or provide) so that, when the owner is determined, the money may be provided to the new owner. What you don't want to do is just sit there and not pay your rent.
Hope that helps.