Thanks, old34! By the way, is it true that after the recent crackdown they are sending everyone home to get their new permits as far as Shanghai is concerned?
No one gets sent home to get their new permits. Permits are issued in China by the local PSB. Are you asking about Z-visas? Z visas are issued by the embassy or consulate in your home country generally. You'll need a Z visa (not an L or an F) to apply for the Residence Permit (RP) within 30 days after you arrive on a Z visa. If you are already in China on an L or F, the rule for the last couple of years has been you have to exit China and get a new Z visa and re-enter and then proceed to get the RP.
If you're in China and already had your Z visa converted to an RP, your next employer can roll over your RP to themselves by following certain procedures. (The RP follows the employer.) The RP, BTW, serves the same function as a multi-entry visa. You can come and go on it as many times as you like.
The last Z visa I had was in 2004. After that, I have been living and working here continuosly on renewed and rolled over RPs. And I've left and come back to China a few times on those RPs.
Continuity is the key. Break the chain, and you have to leave and go through the whole process again.
Word is that in some areas, the locals will convert an L or an F to an RP without having to leave. I doubt that's true in the bigger cities these days. Rumor is, in some cases you don't have to return to your home country, but you do have to leave China to get a new Z visa issued by a Chinese Embassy or Consulate outside China. Hong Kong, for visa purposes, is considered "outside China."
The 2 key issues on this method are these:
(1) The letter of invitation, issued by the local Foreign Experts Bureau, directs the Chinese Embassy to issue you a Z visa. IT MUST BE ADDRESSED SPECIFICALLY TO THE PARTICULAR EMBASSY TO WHOM YOU WILL APPLY. In many/most cases they will simply type in the name of your home country based on your passport. An American showing up in Hong Kong with a Letter of Invitation addressed to the U.S. Embassy will find himself summarily back on the bus to Shenzhen. You and your FAO must be active in telling the FEB to address the letter to an alternative Embassy/HK if you are trying to go that route. Some local FEBs don't like to do that or can't because of local policy. Thus those areas which absolutely require you to return to your home country.
(2) The "outside China" embassy or consulate or whatever they call it in Hong Kong, must agree to issue the Z Visa to a non-national (i.e. of their own country). Some of them, even though they have been "instructed" by the FEB letter to do it, will refuse. The Chinese embassy in Korea, as I understand it, imposes additional requirements related to how long you have been in Korea and how long your remaining Korean status will last. Hong Kong has been known to disregard the "instructions" for some nationals and those coming from some areas of the Mainland despite the "letter of invitation."
In short, the info on the Internets is all over the place. Much of the confusion is due to the the inability of people to accurately use the proper terms. A Z-Visa is not an RP is not an FEC. They are different things involving different ministries, bureaus, and branches. As noted in the two keys above, in some cases, mileage may vary, but now you know why. And in most cases, it is not advisable to rely on outliers.