Binance is first and foremost an altcoin exchange and has very little to do with bitcoin. and the day they shut down is going to be the repetition of dozens of other bigger exchanges shutting down in the past and won't affect bitcoin.
You said "and the day they shut down" - so in your opinion it's only a matter of time before they shut down or there is a chance their business can last for years and years from now on?
How do you see their chances of staying in the market?
my prediction is that all centralized exchanges will become obsolete in somewhere between 5 to 10 years from now specifically the altcoin exchanges such as Binance. there simply is no reason for anyone to go to a centralized exchange to trade bitcoin vs. altcoins or altcoins vs. stable coins. the movement has already started too with the decentralized exchanges growing slowly for now.
but more specific to Binance prediction is that it will have the same fate as all its predecessors. there simply is no difference between Binance and Mt-Gox, Cryptsy, Btc-E, Poloniex, Bittrex, .... each of which were gigantic in their time and some day they either scammed and went away or scammed and lost their #1 position (replaced by another).