They have to get a license to do so. And the foreign applicant has to get an expert certificate to prove they are an expert in that field.

The Foreign Expert Certificate is issued by a Government Agency after completion of all requirements and at the request of either a company approved to hire foreigners, or a foreigner seeking employment.

I never heard of a private company in China allowed to issue a FEC, but it would not surprise me at all if it is done.  The wonders of "guangxi" I guess......

I understand the question to mean that can any legally operating Chinese company issue cause a foreign expert certificate to issue (from a Foreign Expert Burea).

First, the company needs to obtain an alien labor authorization permit from the local Department of Labor.  This is not an easy task as the local Department of Labor will consider all kinds of facts, like whether or not any Chinese local inhabitant can be found to do the job within "x" period of time, etc., etc.

Then the company will need to obtain a certificate from the local Tax Authority that the company has run a profit and paid taxes for "x" number of years (some places 2, other places 5).

Then the company will need the authorization of the local police authority, equivalent of corporate good conduct certificate.

With all of this they will go to the Foreign Expert Bureau and apply for a Foreign Expert Certificate and then it will depend upon a great number of things.

My employer never applied for or issued me an expert certificate. They told me it isn't neccesasary. I can't find an answer for this. Please help. 

If this question is "Can any fully registered Chinese company legally employ foreigners?" the answer is no. Some can providing the position to be filled fulfills specific governmental guidelines and the company registered capital is high enough. If this was not the case, there would be all kinds of abuse and scams related to Chinese companies obtaining work permits for foreigners and taking substantial payment for doing so.