There are 6 things I can think of that will make a capacitor fail like that:
1. It's installed backwards. This would usually cause an instant failure.
2. Ripple current too high (more capacitance needed or better quality cap needed). This usually happens over time.
3. Shorted rectifier, so the cap was exposed to AC. This would be caused by an overload condition. If the cap is in a tube power supply circuit, could be a bad tube with a heater to cathode/plate short for example.
4. Extreme over voltage. I'm not familiar with the design, but could also because of a shorted tube if that cap is for the heater supply.
5. Loss of transformer center tap connection in the case of a split winding. Again, I'm not familiar with the design, but this can also happen if the circuit board depends on a chassis ground and a screw wasn't tight enough, or there was paint on the chassis where there shouldn't have been.
6. Internal transformer short. This can develop if a high voltage winding is left unloaded, specifically in the case of a plate standby and/or there is insufficient insulation between transformer windings.
Anyway, I've seen that type of failure in all of those cases on various electronic devices.