Why would anyone take a job at 11.70/hr when one at 20$/hour is available? This makes zero sense.
It also means far less job security for anyone who has such a job, because there are so many seekers employers will hold all the power, and will fire people easily. So it's also a high-stress job, but presumably worth it for that pay.
Which also answers your question: People will take lower paying jobs in order to have a bit more flexibility to request time off, or to make mistakes without fear.
If this is a global floor in California, it's going to lead to some interesting things.
It will have the effect of flattening out the income of a huge chunk of society. A huge number of people in California will all have identical income.
It will be cheaper to make things across the border and import them. So the kinds of jobs needed will change. California will lose local jobs but gain jobs having to do with coordination and importation.
Are we living in our own little bubble much?