Google funds basically all of Mozilla's budget, something like $300M/yr. Google does not consider Mozilla a rival. If they wanted to destroy Mozilla, they would just need to not renew their funding agreement.
One of my close friends works for Mozilla. I was told by him that they need to spend most, if not all of their money every year. So I don't think they have a substantial amount of money in the bank.
Google hugely benefits from Mozilla search deal. I am sure companies like Amazon, Yahoo and Bing shall jump to the opportunity.
Firefox, IMHO, is one real challenge to Chrome with IE to be outed the day most of the Internet is educated to better software and starts to learn making choices in a broad manner. Safari not counted of course. So, as I said that leaves Firefox and Chrome in the arena. And a Firefox wounded with a financial blow shall be meat for Chrome. Things that's keeping Firefox in race and that is innovation, freedom, privacy advocacy. Without much money in the bank or boggled with court cases it's going to be real hard.