|Eddie, are your referring to "cathode stripping"? (I put the term in quotes, because some people believe that the concept is misleading or perhaps bogus.)
The basic idea, as I understand it, is that when B+ plate voltage is applied with the cathode not fully hot, the cathode can be damaged. I visualize electrons being physically yanked out of the cathode when thermal emission is low - but probably that is an overly simplistic explanation.
:If you reduce the filament voltage more than a few percent below rating - it will accelerate cathode depletion and the tube will wear out faster.