Are you in Mexico Illegally? You can Fix it.
Illegal immigrants in Mexico can fix their immigration status without fear of deportation. "Rather than deporting people who don’t have authorization to be in the country, there is a process for “regularizing” (illegal) immigrants. According the (Mexican) law...illegal immigrants are “never” arrested and sent to jail unless they have committed a crime in Mexico or in their home countries." The process includes paying a fine and filing the appropriate paperwork.
The bottom line: As long as the US Marshals are not after you, you can stay in Mexico.
Side note - Looks like the largest number of illegal immigrants in Mexico come from north of the border! Read more here.