It depends on what you mean by "long trip". If it's out of the 5 boros and Nassau, then you can negotiate the price and can't just say "twice the meter", so in that case, yes you can (I.E. someone wants to go from Penn station to some place in Suffolk county).

It happened fairly recently, some guy asked a cabbie to take him from NYC to CA. He paid the cabbie 5K, not sure if he got the money up front, but they negotiated it before the trip.

Wow, "Ask The Shack" has given you some very bad advice. It is not legal under any circumstance to require payment in advance. A "long" trip like Penn Station to Sufolk does require a pre-negotiated rate, but you can't ask for that payment in advance.

It is acceptable to "negotiate a rate, agreeable with the driver and passenger if the trip is out of the 5 boroughs and nausua and westchester county". As far as payment in advance, well i dont think there is a rule that states that no "Flat fare to be paid at arrival of trip". Of course for within city and Rate 4, payment is made what is shown "at meter and drop off". Need to recheck the rules but i beleive this is the situation. if it doesnt state it for a flat fare ride(excluding JFK), i dont think there is nothing against it..i would see it as "part of the negotiating",