Notorial,
You're wrong about California....the right of redemeption end the day of the tax sale. What you say in most other states would, nonetheless, be correct. Right of redemption varies greatly by state (MI for example is 18 months) Here is a link to the LA county Treasury and Tax Collector Auction FAQ where I found this info.
http://ttc.lacounty.gov/Proptax/auction_faq.htm
Assuming the FAQ is correct, one could be the winning bidder and as soon as the tax deed is received, file a quiet title action in court to perfect the title.