If you are in the middle of doing something on your Mac and Firefox suddenly crushes, this could be really annoying. However, if an error message shows up every time you try to launch an app again, there is nothing left apart from reinstalling the browser.
Considering the fact that Firefox always leaves some data on your computer, the best way to reinstall it is to use an app which can erase all the Firefox data completely.
In some cases the message “Firefox quit unexpectedly” could be due to the Mac security update. This might happen when your Mac’s firewall (the security protection software of your Mac) used to recognize older Firefox versions but it does not recognize the latest one. To fix this issue, you should check the official Mozilla instructions: https://support.mozilla.org/en-US/kb/configure-firewalls-so-firefox-can-access-internet
In case the Firefox unexpected crashes continue, you should contact Apple support for further assistance.