If you had a conditional PR, for example a business class where you must live in and run a business in the province then you must meet those conditions or you lose your PR.
If you were just a regular Quebec or other province selected immigrant, they normally do not do anything to you but if they wanted to, they could accuse you of misrepresentation at the time you applied and landed and that could lose you your PR. For the province to prove that you misrepresented yourself would be harder and harder the longer you stayed in the province. Say you stayed in the province for 6 months or a year and you could not find a good job, you were working in telemarketing or a fast food place and then found a good job in another province, they could not really blame you for leaving. They can not prove that your intent was not to settle there when you landed. If you however stayed in the province for 2 weeks before moving to another province, it would be easier for them to say that you obviously did not intend to settle there when you landed and therefore have misrepresented yourself in your application. I have not heard of them going after anybody like that but they could if they wanted to.
