Mozilla is going to be around as long as there are people using and developing it. It's OSS, you can marginalize it but not kill it.
The way to keep it thriving (because it is, 9% market share is tens to hundreds of millions of users) is to empower developers to keep it relevant and users to escape the Google ad Imperium and universal tracking.
The day Mozilla announces chromium support, there will likely be a hard fork. It will also be the day where they fire/lose most of their team. That would be after users walk away from it. It would be suicidal. It would kill Mozilla the organization but you can bet somebody will keep the browser going.
Worst case, Google pulls their funding at some point. They are under no obligation to keep on funding it. Mozilla might need to diversify their income at some point or scale down their operations.
Apple and Mozilla being around will force Google + MS to play nice. Also the latter two are frenemies so the most natural place for them to cooperate is through open source and standard bodies. MS has had a big impact on web standards historically and they are unlikely to leave all that to Google. So, it's going to continue to be a four way discussion in the standards bodies. Chrome as a reference implementation will become even more important than it is today of course.
The real question is whether Apple will continue to keep Safari alive. With shrinking sales and many mac users option for Chrome/Firefox anyway, they have a problem there. They might decide to join MS and retire webkit. Right now it's usage is inflated because Apple bans competing browsers from their app store.