Capacitive dropper.

[G6Tanuki]

Half-wave-rectifying the heater current was used in quite a few TVs. At least one series (Thorn/BRC 1500?) guarded against diode-failure by a coupling from the heater-chain to the frame-timebase - if the diode failed it resulted in AC being fed into the frame T/B - the resultant frame instability made the picture unwatchable so hopefully the viewer would turn it off before the heaters suffered from prolonged over-dissipation.

[Argus25]

It is really totally unnecessary if you use a half wave system to add any sort of diode failure/ protection devices with the types of diodes you can buy cheaply nowadays:

https://www.vishay.com/docs/86003/by228.pdf

Just for example the inexpensive sintergalss BY228 , made for energy recovery applications is 1500V and 3A rated. It will never likely see any condition in a mains operated heater chain that will destroy it, not impossible of course any part can fail, but in this case it would be more likely the whole radio or TV would be beamed up by an Alien, than the diode short out in this application.

Then if you were still worried about it, you could go for two 1500V diodes in series or even three since the dissipation is very low and reduce the probability of failure so low that it barely existed and for practical purposes was zero.