| No, capacitor die independently of the tube. It was or glass cracking or transistors and the mains fuse - in such regime transistors overheat, fail short circuity and then the fuse has to act and disconnect the supply.
And here came (one hypothesis i got recently) the difference between 120V and 230V designs:
As 230V designs use bridge rectifier, such transistor short cause very huge (virtually unlimited) current flowing from the mains (>10A), so there is enough margin to blow the fuse.
But on 120V designs there is voltage doubler, where 2 diodes from above are replaced by 2 capacitors. When the DC output is shorted by dying transistors, the current is limited by capacitor's impedance, so might stay low enough (<1A), so the fuse does not act. But even with such relatively low current, the power dissipated is very large (1A cause up to 120W dissipation), what turn into heat in the ballast compartment (designed for <1W normal operation power dissipation), so it overheat, start to smoke or set a fire.
And as fuses have quite some tolerance, they have to be designed so, under normal operation they never trip, even if the tolerance cause the trip current is on it's minimum. But this mean, then it's maximum is much higher then operating current, usually >5x. But with the doubler (limited failure current) this mean, then the fuse might not trip at all, so we have a fire.
The cure would be adding two diodes, each in parallel with one doubler's capacitor, so when the short appear, these diodes ensure high enough failure current, so the fuse reliably trip. But these diodes cost a cent each, so are often assumed as too expensive for components what normally have no function, so omitted...
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