That is a very ugly corner they backed themselves into, with massive “help” from Mother Nature (Gee, thanks Mom; you really shouldn’t have!).
Under the simplest base case in US regs, which are not universal …
The general concept behind preflight planning on nice days is you land with 45 minutes of fuel aboard, plus a few more (5-10) minutes for extended vectoring or slowdowns around the destination that are statistically likely.
If the weather sux (technical term), you are required to designate a different “alternate” airport with sufficiently less sucky (technical term) weather. And carry enough fuel to try to land once at the destination, then fly a plausible route and altitude to the alternate, then land there, with the 45 minutes fuel still remaining.
If holding is reasonably foreseeable, there’s another planning bucket for carrying hold fuel, anywhere from zero to 1 hour or more. Which can legitimately be fully expended on the way to the destination if needed. But which represents all of your normal safety cushion before you start getting into the abnormal last-ditch safety cushion of the 45 minutes. So the wise pilot is increasingly uncomfortable as the hold fuel dwindles and is actively working on changing that trend by doing something different than just sitting there being led around by ATC.
That’s planning. There is nothing legally preventing making a second attempt at the destination, which fuel is coming out of the 45 minutes, then making a run to the alternate when that too fails. But anybody with a brain knows they’re playing with fire if they do. If the reason for the original go-around was a one-off, like a truck pulled onto the runway in otherwise adequate conditions, you may be safer to take a second shot at the destination, rather than opening the fresh can of worms of going elsewhere. OTOH, if the weather is chaotic, bad, and expected to be long-lasting, the failure of your first attempt strongly suggests the second will be equally bad. In which breaking and running for the alternate is the wise thing to do.
As a practical matter, In 30+ years of doing that job I actually diverted after a failed landing attempt probably once or twice. And it instantly became dicey (as expected) because the planned fuel consumption to the alternate is predicated on a probably more efficient routing and altitude than you can get from ATC in the teeth of a big airport having a weather meltdown. By the time you do get there, what looked good on paper 3 hours ago looks a lot less good on the fuel gauges now.
Far more often what happened in our operations was you’d be holding at some high-intermediate altitude 100 miles short of the destination. And running forward calcs for “If we left holding now, what would our fuel be at touchdown, with some fudge factor for crappy vectoring near the destination?” As that number counts down towards the planned burn from failed destination landing to alternate airport, plus 45, plus a fudge factor for vectoring at the alternate, we begin planning to go somewhere else. Which may be the planned alternate, or may be yet another airport more conveniently located for where we are at the moment.
The big point there being that as the fuel along the planned routing gets critical, we cut and run to the alternate or other selection, without having burned the planned fuel to go from our present position (holding?) to the destination, then fail to land. Such that the moment the diversion starts, all our fuel concerns usually evaporate; we’ve just gained a large dollop of “just in case fuel” by the flying we just avoided.
In scenarios with few nearby airports at all, or few nearby airports with significantly better weather than the destination all this can get kinda tense. You win that game by being waaay ahead on making multiple contingency plans, evaluating each continuously and by being spring-loaded to run away once the trend starts leaning increasingly towards failure, not success. Far better to run than stay and fight to the last drop.
Burning into reserve (or recognizing that you will be before you get there) is not a per se emergency under US regs. But it is a sign of a rapidly deteriorating situation, and warning ATC of that is desirable. In many countries, an emergency declaration (“Mayday”) is the approved way to do that.
As always, the “right” answer is to have used superior judgement an hour ago to avoid having to do a desperate act of superior Yeagerism right now. But if they already missed that offramp, whether through bad skill, bad luck, or both, your point is well taken. What now, Batman?
An off-airport landing, and especially one after the engines quit, will be a multiple fatality event. The Air India 787 crash a couple months ago is a decent example of that scenario. Your odds in a river, lake, or near shore ocean are far better if one is available. Ask Sully.
An attempt to go around with very low fuel states may result in immediate fuel starvation; the tank outlets are set up so the last dregs are available while descending, not climbing. The big nose-up of a go-around, the fuel sloshing aft due to accelerating speed, and the simultaneous great increase in demanded fuel flow may have you start sucking wind right then and there.
All of us have discussed being in a must-land situation with low ceilings or vis. Taking an ILS or RNAV approach way past the published go-around point all the way to a blind flare & touchdown / impact is a high risk, but probably no-injuries resolution to being just about out of fuel.
If the issue is more like crazy winds, there’s a certain amount of above-normal flailing you can do to try to force the landing to work after you’d much rather have declared a go-around for a second try but fuel prevents. But, as we saw with that Korean 737 recently, an attempt to land that finally gets all the wheels on the runway with 2/3rds+ of it behind you guarantees you run off the end at speed then almost certainly hit something unforgiving. Which is also, absent EMAS, a guaranteed multi-fatality outcome. Even with EMAS, there is some (unknown to you) speed beyond which you coming out the other end is an engineering certainty. I’d sure rather go offroading into the bush, or out into a city doing 40 knots versus 140. But it’s still gonna wreck the jet and hurt a lot of people.
These kinds of extremis scenarios are generally not formally trained or planned for. There’s nothing to look up in the book even if you had time to do so. So it’s a combo of folklore and self-introspection on what you might do if you find yourself there. Somebody with little experience or little introspection may never have even thought about this and will probably blindly do the standard thing and run out of fuel during the go-around followed by an off airport impact.
There’s an old saying about running out of altitude, airspeed and ideas all at once. There oughta be a a 4th factor in that list: Fuel. But when you’re out of ideas, carefully considered pre-planned ideas, you’re probably screwed even if you still have enough the other three. Get short on any of them too and people start dying real soon.
I know of other close calls on fuel remaining. But this is the worst I’ve read of. Seriously sucks to be them about now, but they are alive & so is everyone else.