I don’t believe so. Not in the foreseeable future. It’s impossible to say what will happen to Firefox over the longterm (or Brave which is much newer, smaller, with a less certain/not-yet-fully-realized or sustainable business model), but so far, Firefox has demonstrated a lot of staying-power, and persistence, and they currently have a positive revenue/expense ratio.
There are no guarantees for any of the browsers not backed by big tech, but Firefox is in a better place than many derivative browsers, and is the only independent browser to persist in a market that is extremely weighted towards the big-players.
What about browsers like TOR and the Mullvad Browser?
These projects are heavily dependent on Firefox, they couldn’t exist as they do without Firefox. I don’t know what they would do. Projects like uBO would also be handicapped by the disappearance of Firefox.
What would happen if the browser just shuts down?
Google achieves a monopoly on non-Apple OSes. Google and Apple achieve a duopoly in the browser space like they currently have in the smartphone space. We would lose maybe the last remaining, non-commercial, pro open source, pro net neutrality, pro privacy voice at the web standards level. This is really important because what happens at the standards level affects everyone. Brave or some other derivative of Chromium can try to undo some of the anti-user or privacy-undermining features Google includes in Chromium, but they are somewhat powerless if Google is able to impose their will at the standards level. At least that is the risk. A lot of this is speculative, so you’ll get a lot of differing perspectives.