Consider leasing something.
Typical examples are a three-year car lease or renting an apartment.
Although there is no "down payment" per se, typically, a lessee does put some sort of security deposit or enter into a contractual agreement that limits an overuse.
For example, a three-year car lease might limit per annum mileage the vehicle can put on.
An apartment landlord might stipulate the right to examine any damages and request compensation or the right to restore the unit to a clean condition in a leasing agreement.
My question is:
In either case or in any leasing situation, can a leased asset be collateralized?
My immediate response would be "no", because you cannot collateralize something you don't even own. In the car-lease example, the lessee does not own the car until it is fully paid for ownership at the end of the three-year lease. In the case of renting an apartment, this is also not possible unless it is some sort of leasehold property in Maui.