All embassies have police personnel on site that conduct investigations for passport, visa and ID theft and fraud as well as anti-terrorist concerns. In the US Embassy that is the RSO or Regional Security Officer and they do in fact work in conjunction with Chinese police on some matters. INTERPOL is also an agency that investigates situations where passports are being stolen, or data is being collected and sold on the black market.

Before posting comments without knowing what you are talking about, I suggest that you do some research. The US Embassy also has IRS, FBI and DEA federal agents on staff as an example of the many law enforcement agencies working out of the US Embassy in Beijing. For a rapid education, you can contact Barry Moore, of the US State Department at the US Embassy in Beijing. He is the RSO there. Special agents of the Homeland Security Department are over at the Kerry Centre as another example, and one of many.

Do not confuse the average "diplomat" with armed federal agents performing law enforcement functions at any given embassy.

If someone in any nation is doing something illegal that MIGHT involve stolen passports, a file is opened by the host nation and the country of interest.