A visa is not attached to a particular company. Once it is issued, you can use it to enter.
Note that this is different from an extension of stay which is done at a local Thai immigration office. Extensions are tied to the reason of extension. So if you are extended by reason of employment, the extension is voided as soon as your employment ends (fired/quit). Similarly, if you extended by reason of marriage, that extension is invalid the day the divorce is finalized.
You dont automatically get 7 days to leave the country. You must apply for that 7 day extension at the local immigration the next business day.
This is why some people opt for a Multiple Entry [ME] Non Immigrant visa (Non-B in your case) vs a 1 year extension of stay. If you get fired or quit, your visa is still valid. Just tell your employer that every 89-90 days you will need time for a border hop.
Not sure how easy ME Non-imm will be to get for Indian national though. Even if they do issue ME non-B, sometimes the neighboring Thai Embassies will want to see 8-10 months remaining on the work permit as a condition to issue ME.