How is BTC-E a $4 Billion company? That figure counts the total transactions made on that site for a few years, not their total asset. As for covering $110 million, I took a quick count of their earning in fees. So, before they went offline, their daily volume was about $56 million on all currency pairs. Since there's no maker-taker system, it's safe to say that they earned about 0.4% (0.2 for two sides) for most of the transactions. That brings them about $224K in daily earning. Let's be nice and assume that this is their average day and without taking lower price or volume into account, it will take them 500 days to cover $110 million. This is while covering operational cost which definitely won't be cheap.

All in all, I don't think they will be able to continue unless they levied the cost on the users but even then it's still hard to function without profit for the next 1.5 years. The only way I can see it will go well if they either take a plea deal that reduces the fine to a more manageable amount or just ignore the whole ordeal and becomes more rogue than ever while still maintaining trust from bitcoin users in general.