A Singaporean friend who works in hong kong has been living in Shenzhen last 15 years or so very much like Singaporean living in JB using short term visit pass valid for 30 days, that could be renewed by getting out and then back into China. This is easy if you live near Hong Kong or similar border immigration check points.
In addition to ways to stay in China suggested by other forumers here, I have known or heard of foreigners who get to stay on longer term doing charity or NGO works, teach English, sign up for kongfu or Buddhist classes at some shaolin or wudang temples, do small business, using similar means many foreigners use to stay in Singapore, etc. Sorry I do not know more comprehensively. I guess it is good to clarify with the Chinese embassy here.
江南水鄉-周莊 01
http://m.youtube.com/watch?v=WsIXmDY78a8