Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and in older literature are sometimes referred to as "thermions". After emission, a charge will initially be left behind in the emitting region that is equal in magnitude and opposite in sign to the total charge emitted. But if the emitter is connected to a battery, then this charge left behind will be neutralized by charge supplied by the battery, as the emitted charge carriers move away from the emitter, and finally the emitter will be in the same state as it was before emission. The thermionic emission of electrons is also known as thermal electron emission.
The themionic emitter is not depleted by loss of electrons as electron is essentially a point particle and contributes not even fraction of a percent towards the contitution of atom and thus the depletion of material is essentially nil even if its all the electrons (hypothetical case) bound as well as free are emitted.
However,its depletion do takes place due to loss of matter owing to the vaporzation of external surface at elevated temperature over a long period of time.