I have got my Non Immigrant - Business visa extended until November but my work permit expires in September and so does my work contract. If I plan not to work and extend the work permit, will I be allowed to stay in the country until my visa expires or I have to leave when the work permit expires?

If you are on an extension of your permission to stay based on work, the extension ceases to be valid once your work ends. The answer to the question you posed in the thread's title, however, would be that the visa, and permission to stay based on it, remain valid. It is another illustration of the importance, sometimes, to be very clear about the distinctions between, visa, permission to stay, and extension.

As said above ... 

• IF you have a valid visa it can be used until it expires.
• An extension of stay is invalid from the day work stops or the WP ceases

In your case it would seem the latter applies as you do not have a valid and you must therefore, leave the country.

How would immigration know that the work permit expired earlier, if one was to leave the county in November at the end of the visa? I didn't think that the two are linked by computer, but could be wrong. I would have thought that the WP permit is cancelled and then some papers are taken to immigration to cancel the visa. Then one needs to leave. 

37 minutes ago, DavisH said:

How would immigration know that the work permit expired earlier, if one was to leave the county in November at the end of the visa? I didn't think that the two are linked by computer, but could be wrong. I would have thought that the WP permit is cancelled and then some papers are taken to immigration to cancel the visa. Then one needs to leave. 

I think you are correct that, in most cases, you would get away with it. Many might well take the risk of relying on that. The fact remains that you would technically be on overstay, subject to fine, deportation and blacklisting if discovered. It would, especially, be unwise to try this if leaving your employment under bad terms with a vindictive employer who might turn you in.