I really am interested in hearing how this guy overstayed by nearly a month. I've lived in China nearly 10 years, and there have been periods when I was extremely poor and could barely scrape money together for a HK run (back when one regularly did such things), but I've never overstayed a visa, not once. I suppose there are some scenarios where I could imagine this happening -- but really, even if you have some sort of emergency situation, maybe you're broke, or you lost your passport, or you are being held hostage by a school, still, you contact your embassy, explain the situation, and beg for help before it ever gets to that point. You (and I assume this dude) are in Guangdong so I honestly can't imagine what stopped him from getting on a bus or a ferry, hopping across the border, stamping his visa, and hopping back. The cops are probably going to wonder the same thing.
Maybe he could just play it off as "super dumb foreigner who didn't understand his visa type" but that's a stretch.
I still think I'd take my chances with the border cops before I'd turn myself in locally. If it were a visa about to expire, no way to get across the border before tomorrow, I'd say go to the local entry/exit and ask for an extension, but at this point the deed has already been done. Guy needs to get himself out of China asap to prove that he has the intention of leaving. If he turns himself in I think he runs a much larger risk of finding himself being locked up or forcibly escorted out of the country. They're not going to give him another visa so he can stay put and overstay that one too.