What are the legal implications on a tenant if she did not provide 30 days written notice of non-renewal after the lease has expired?

Most leases become month-to-month even after they expire, so you would still be bound to the notice required in your lease. In California, state law requires that renters give a 30-day notice, doesn't matter what the lease says. You would be responsible for giving a 30-day notice and paying through the 30 days, even if you are not living there. One exception, if they re-lease the apartment before the 30 days is up and someone moves in, then you will only be responsible to pay through the new resident moving in. Landlords can't charge two people rent for the same apartment.