Rents didn't really drop but housing prices did. The closer to SF you are, the less they dropped. Housing prices had recovered by 2012-ish in SF proper, but are probably STILL not back to where they were in places like Morgan Hill.
OTOH I was paying 1385 for a one bedroom apartment in San Carlos just a couple of years ago.
I can't find it right now, but some SF neighborhoods did see rents drop. I remember seeing data for Noe Valley. Basically tenants went to their landlord and said "Give me a rent reduction or I'll move to this apartment that's nicer and cheaper".
That's interesting, but it makes sense -- SF is a city of primarily renters. In more suburban/residential areas, rents went up because people lose their houses and needed somewhere to live. Supply went down, because there was more demand for rental stock but the foreclosed houses largely sat vacant for months or years.
(I actually did 'negotiate' a rent decrease in ~2008 in Santa Clara; they wanted $150/mo MORE, so I pointed to a unit on their website that was $120/mo LESS, and said I wanted to rent that one instead. Needless to say, they made me an offer to stay put, thank god.. having to move across a parking lot would have been miserable. But of course rents in general took off despite this small blip)