Legal Question in Real Estate Law in California

No, you do not have to be current, but you should tell the tenants so they can make a choice as to whether to remain there or not.

No.

The "no" answers are sorta correct, but in my opinion, there's more to be said about the issue.

First, it is illegal to engage in "rent skimming," which is defined in the Civil Code at sections 890 to 893. The definition includes pocketing rents received during the first year of ownership without paying an equivalent amount on the mortgages affecting the property. This is a civil wrong for which an affected tenant has civil remedies, and can be a crime if the landlord engages in multiple acts of rent skimming.

In addition, leases ordinarily carry with them an implied covenant of "quiet enjoyment." This does not mean a guarantee against noisy neighbors..... it is, rather, a warranty by the landlord that your right to possess and use the leased premises during the term of the lease will not be challenged by someone claiming a right superior to yours in the premises. A foreclosure proceeding is a violation of that right and a breach of the covenant, and arguably the covenant is breached and the right impaired as early as the recording of a notice of default by the unpaid lender.