Firstly, let me preface this with the fact that I am not interested in chastising the user, and I am not interested in looking at the original source of the arc (it was a tool accidentally breaching the power rails). This question is EXPLICITLY about suppressing a PCB arc once it has started.
Someone had a significant fire on a board they built. I helped with the layout and so on for the power switching. The board works very well, under normal use.
The cause of the fire was an accidental user (builder) induced short between Vbat and ground, with a 100A fuse (required because this board pushes several hundred phase amps, it is used on E-motorbikes). These boards do not spontaneously burn. The creepages between traces are 0.25mm on the high power stuff, board intended to run with 20s lithium so 84V max and the FR4 is V0 with thickness enough to meet insulation requirements.
Board is open source, and files can be found here. The https://github.com/badgineer/CCC_ESC
What you can see has happened is that an arc started at the top of the board, and gradually eroded it's way through the board over the 10 seconds it took for the builder to pull the battery plug. The arc was between the Vbat power plane and the ground plane, which for the purposes of extremely low parasitic inductance are overlapping.
When I build things like this professionally, the whole lot goes inside a fire rated enclosure, and burn tests are carried out to prove it can contain it. This is a different case, because it is built by DIY hobbyists who may or may not do this (in this guy's case, the thing was surrounded by metal that probably would contain the fire, but this is not guaranteed in general).
What I want to know, is how a board can be designed to not propagate an arc once it has started. Are there layout techniques/known thicknesses of inulation/treatment chemicals/self quenching materials/.... that would stop this?
Fuses are a dead end, the arc takes way less current than the normal current in use. Conformal coating is a good option for prevention, but probably does not quench the arc.
Otherwise (and this is probably advisable anyway) the advice will have to be: "Put the damned thing in a metal box or suffer the consequences".
This is a remarkably common problem among the DIY community, searching forums shows up any number of brands from any number of countries and any price band burning.
EDITs: A lot of commentary on the creepage distance has come up despite the clear statement that this is NOT a creepage issue. I will address where the clearances chosen came from. UL61010, the standard governing laboratory devices, which is what I usually work to, excerpt below: At the max recommended 20s battery, 84V, basic insulation is met, and is close to reinforced insulation (depending if you interpolate or take the next highest category). I have highlighted the Mosfet breakdown voltage, 100V as a ballpark "where we stand".
I am coming around to the idea that this standard is not applicable to lithium battery powered things, but, it would have made ZERO difference to this case if the creepage distance had been 0.25kilometers not 0.25m.
The large creepage distances referenced in answers are for mains grid connected circuits, where there is a high probability (certainty) of massive overvoltage from lightning, substation failures, the factory down the road load dumping etc. Battery powered devices with 3000uF of capacitors and over voltage shut down are not susceptible to such over voltages. Whether this logic stands or not, I am unsure, since I don't work with big batteries for my job and have not formally investigated it.
EDIT2: The creepage thing continues, so I went and found a SEVCON Gen 4. I picked this, since I understand this is what comes in a Zero motorcycle, which has been through type approval testing with a notified body, and is being sold "en mass" in the UK, US, Europe... Quite obviously, the creepage distances do not add up to the 2.1mm suggested by the top answer below. Probably the creepage is closer to 0.5mm and the board has overlapping power and ground planes, like this one. What it DOES have, is a case that looks like it might contain the mess if it went up, and would certainly stop anyone getting errant metal in.
EDIT3: At this point, I will let on how this happened, the user had a derp moment and tried to solder on the blue wire that is hanging off in the pic, while the battery was plugged in. This shorted across the ceramic cap with a whole load of solder, started the arc right at the edge of the board and things proceeded from there. The solder pads are being moved. Not the nicest bit of design, not the smartest thing to solder it while plugged in, but there we go, accidents happen.