If the company has hired you from your country then all depend upon the company to send you back home or release you weather it has no project or due to any reason.
The compnay can provide NOC to join another company on its own visa but the existing company will not loose its visa as the government has fixed visas for each company in doha. Getting NOC you will be exempted from 2 years ban for re entry.
Wishing you best of luck.