Highly illegal and HIGHLY common. When my wife moved here (I uprooted her career because of our marriage), she spoke to a few of these people. It was way easier to get an illegal job, and better green card prospects (don't know why).
This is a huge problem by itself. H-4 EAD after I-140 is not enough because that forces you to stay with your current employer until you get your I-140. If you are going to restrict H-1B to highly skilled immigrants, then H-4 EAD should be eligible for any H-1B holder's spouse regardless of I-140 status. Otherwise you are basically saying "we only welcome highly skilled immigrants that are single"