No legal obligation at all. Even if you lose property they are protected for the duration of their lease.
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You aren't required to disclose anything to your tenants, and as logn as you own the property, you can collect rent, etc. if your mortgage is foreclosed, the bank will own the property and will sell the property to a new landlord or operate it themselves until they can sell it.
The tenants have protection under CA law, especially if they are in good standing with their rent payments.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.