Anyone can set up a sole proprietor business. But you would need to have an appropriate visa to be employed by it. In principle a Sole Proprietor business can sponsor a visa just as any other can, and in rare cases you can get it through ImmD.
For example, I have a friend who had been in HK on an Employment Visa for a few years until late 2008 when he was laid off. He was quite quickly able to get contracts for some consultancy work in other countries around the region (whilst continuing to reside in HK on his unexpired Employment Visa). He went to ImmD and asked them to allow his business (I'm not sure whether he established it as a Sole Proprietor or a Ltd Co to be honest) to sponsor him, despite the fact that it had no plans to employ anyone else. And they did so. I think even he was surprised, but he put it down to four factors:
- he had already been in HK for about 4 years and it was clearly where he wanted his long term home
- he was open with ImmD and made it clear that he wanted to work within the rules
- he had readily obtained contracts for work around the region and could show that he would get some in Hong Kong too
- the economy was in a bit of a mess at the time and ImmD was seeing far, far more foreigners leaving than arriving.
As far as I can tell this sort of thing is quite rare, so I wouldn't bank on it, but it seems that it's worth a try.