Is there any close event of firefox browser ?

I guess I'm kind of confused. Are you developing a webpage or a firefox add-on (although the jquery part makes me think you are making a webpage)? There isn't any way to detect when the application quits, since all javascript stops running once the webpage is closed. However, you can detect when the webpage is about to be left, either from the application closing, the tab being closed, or the user going to a different page using the [https://developer.mozilla.org/en-US/docs/Web/API/WindowEventHandlers/onbeforeunload onbeforeunload] event. (also, this works in all browsers, not just firefox).