I just found out that the house I'm renting is not listed as a rental by law. I live in Michigan. In case anything happens, I want to know if anybody can tell me what rights I have?

My landlord is incredibly old as well - what happens if he happens to pass?

Like what happening? How did you find this out? If it is a house, there is rarely a prohibition about an owner renting it.

If the landlord dies, then the property goes into his estate where the executor will need to manage it.

Not sure what you mean as "listed as rental" while not up on MI law as much as others, I have owned rental property in at least 14 states and there is never a "list" to put it on, it is listed as a non owner occupied on taxes for the real estate tax rate, property insurance is paid as a rental home, but no lists.

There were options to put it on hud or other lists but I did not want the governemnt restrictions.

But if the owner dies, the new owner ( heir) will have to honor any written lease you have.