how can Bitfinex survive when they cannot receive and send funds to their clients?
They can't and they won't. If people had any piece of sense left in their brains, they would be running away from finex right now. (Smart ones probably do/did) The signs are clear. It is not like Gox which happened instantly without any sign. (Huge price pump caused by Gox was the only sign actually)
The fact that account holders in Bitfinex can move their bitcoins or altcoins off the exchange, as suggested, is an example of how this is absolutely nothing like Mt. Gox. By the sound of most of the posts here, its obvious that ~90% of the people posting haven't been around long enough to remember Mt. Gox. When Mt. Gox went down, EVERYTHING was frozen. Bitcoins, fiat; all of it was frozen. Comparing Mt. Gox to this incident with Bitfinex is absurd. It sucks for Bitfinex themselves but for anyone else, simply get out.