Its not what you think.
A "Frozen Cathode" was often found in battery tube radios where the B+ was applied to the set without the "A" battery being connected. This term dates way back to the early days of radio.
It was a commonly found problem, and could be extremely expensive, as back then a tube might cost a week (or more's) salary.
The filament was "stripped" of emissive material due to the B+ being present and lack of filament/cathode voltage.
That's why you can find battery set tubes, like the 1L6, 1LA4, etc. with continuity but no emission.
Someone connected the "B" Battery and not the "A" or fil. battery.
Also NEVER PULL A BATTERY SET TUBE WITH THE SET TURNED ON.
The surge can blow out the filaments of the other tubes in the set, or that tube when plugged back in. I have seen it happen to others.
Additionally, you can freeze the cathodes of the tubes in the set or cause the tube you just plugged back in to have it's filament blow open from voltage & current surge.
(Think cold start up surge while the others might be at operating temp.)
Now this problem became fairly rare when the AC operated 6 & 12 VAC fil. became standard, but battery tubes were made differently. It could also happen when the 25, 35, & 50 V series fil. were used in the AA5's, but that was rare. Typically in the sets using a pilot lite off a tapped rectifier fil., plugging in a rectifier "cold" could cause 1/2 the fil. to open in it, blow out the pilot lite, or a weak fil. in another tube to fail.