The OP of this thread is now in Mexico illegally
According to the Mexican law (not the forum marms), his status is "pending administrative resolution." The only thing that would make their stay "illegal" would be to leave the country without resolving it. If they were going to "detain" the man, they would have done it at the INM.
Good point re: leaving via the Baja land border without turning it in and OP could probably do that with no problem... apparently the law has been changed as of September 2015 so that this is not technically necessary (even though it says it is on the back of the card). From what I've read, people do turn it in at the immigration office, but if you don't need to according to the letter of the new law, then that's that.
For the southern border, they definitely do stamp you out and definitely do collect the FMM (or fine). Could someone sneak out without resolving their situation? Hey... if that's what floats their boat, why not?