Just know that it can and does happen, the immigration detention centre is full, you can visit the detainees and and bring them food and supplies. Go and check it out for yourself.
If you turn yourself in you will pay a fine, if you are caught by police it's a different story. Police may stop you at a motorcycle checkpoint for example, check your ID / passport and then detain you if your visa has expired. Next you will get to find out just how many real friends you have in LOS.