This is an exaggeration.
Epson's head do not use head, but instead are piezo electric "crystals".
The ink has very little effect on them if it is there or not, other than
a very slight viscosity difference between the ink and air.
The only real damage to come from no ink is if the ink residue dries and
clogs the channels or impedes the piezo plates. In the head were to
have no ink in it, you would be hard pressed to damage the head.
The problem is if the cartridge is removed, two thing occur. One the
ink dries leaving a residue which may clog channels and nozzles, and
secondly once the channels are completely dry, there can be an air lock
in getting the ink to return, if or when desired.
Now, just to be clear, this does not hold true for thermal ink heads
which require the ink to be a coolant, and if the heads are running with
no ink, they will get damaged and excessively hot and burn out or the
nozzles may distort. Thermal heads are either contained as part of the
cartridge, in which case they are "supposed" to be replaced when a new
cartridge goes in with fresh ink, or they are semi-permanent (semi
because all thermal heads eventually fail) (the exception MAY be the new
Kodak head which I've not yet seen a clear design of).
The semi-permanent heads are at most danger of running out of ink,
because they are designed to last many ink cartridge changes and they
also heat up. Examples of these include Canon, and maybe Kodak and some
HP printers. The "disposable" heads which come on cartridges are found
in many HP and Lexmark, and older BJ series Canons, and Dell, which are
rebranded and slightly redesigned Lexmark printers.
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