It looks like I am legally entitled to unemployment benefits following a lay-off. However, my former employer is broke; and it turns out he never paid one dime of unemployment tax/premiums for his employees. Given the circumstances, can I still receive unemployment checks, even though my former employer really screwed up? I live and work in the State of California.

Go to your state unemployment office and ask.

The only employer "exempt" from unemployment, is a church.

So yes - as long as you were a legal employee, over the table, etc, you should still qualify - eventually. You'll probably have to file some complaints with your state labor board.