Technically, when a property is being foreclosed but has not gone to sale, the property is still under the name of the current owner - your landlord in this case. Unless your landlord is rent-skimming, you're still required to pay your rent even when the property is under the foreclosure.
As others have advised, you should not just stop paying rent, as there are some protections for California tenants caught in a foreclosure. However, if you stop paying rent, you may be subject to eviction and other legal/credit consequesnces.
As far as checking to see if your landlord has had a Notice of Default filed (which is generally the first step when a bank starts the foreclosure proceedings), if you send me the address privately, I can look it up for you.
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Generally in Los Angeles tenants cannot be evicted by a bank just because your home is foreclosed on. Los Angeles Municipal Code ch. IV, art. 14.1, Â§ 49.92. This is in addition to the protections offered by the Protecting Tenants at Foreclosure Act.
This is probably a stressful time. But, you do have rights. If you have a valid lease, the bank will more than likely honor your lease. If you're a month to month tenant, you'll have the option of accepting a financial settlement from the bank or you'll have 90 days to vacate.
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Best of luck to you! Keep us posted.