I cant be the first person to think of this...

In my city there is an owner occupant property tax exemption on the first $50,000.  For seniors age 65 and older the exemption is on the first $150,000.   The standard mill rate in my city is 1614.  So the discount for owner occupants is $820/yr and the property tax discount for seniors is $2460/year.  For regular owner occupants the $820/year of savings is not likely worth the effort, but at $2460/year its different.

Let's say I am senior and I want to rent a house. Is it possible for the property owner to give title of the house to this senior citizen "renter" at the same time put a lean on the house for the full value of the house?  I'm sure you would have to be careful how the contract was written to protect both parties.

The contract could be written as an owner financing contract where the senior pays on the house as an interest only loan equivalent to whatever you want the rent to be. I'm sure there are other ways to write the contract. If renter fails to make the interest payment the lean holder could exercise their right to the property and take the title back.

I'm sure there are other benefits or possibly disadvantages to attempting to do this. A few off the top of my head would be the complexity of the contract that would be needed and the time/effort/cost to get it written. Both parties may need the assistance of a lawyer.  The total benefit here is $2460/year. This could make sense on longer "leases", but not likely shorter term leases.

Could this have some benefit to the owner in terms of delaying depreciation? 

This kind of contract could probably only be written by an owner who doesn't have their own lean against the property.