Legal Question in Real Estate Law in California

Once you own the property you can change the rent any way you like. You can also agree with the tenant in advance that if and when you close escrow and own the property certain things will happen. It would be a conditional contract with the tenant, which are legal in any state I know of.

An equitable interest that doesn't give you a current right of possession is insufficient to allow you to make, modify, extend, etc. a lease of the property. The right to lease it derives from the right of possession. Most equitable interests including those created by a final and binding purchase agreement (but not all) are insufficient to create a current right of possession. However, as Mr. McCormick points out, you can certainly negotiate a conditional contract with existing or prospective tenants.