Is it possible for a faulty/worn up Diesel injector to destroy it's corresponding cylinder/piston or other components of the engine or this is just a myth?

I have a "vibrating"/beating when cold injector and someone told me that it could lead to a faulty engine if I don't fix it quickly and I wonder if this is the case or it's just a technical myth. What do you think?

Note that after an "italian tuneup" or some ATF in the fuel the engine purs like a new Mercedes for a few weeks at a time.. The engine I'm talking about is a 27 years old 3005cmc 617.912 Diesel engine.

In direct injection engines, very much so. In an indirect engine such as yours, it's unlikely to harm anything other than the prechamber and glow plug.

Why not just fix it so you don't have to worry about it?

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'79 300SD W116
'86 190E 2.3-16V W201
'92 300D 2.5 W124
'99 E320 4MATIC S210

I am fixing it as soon as possible but I was wondering if it was true or not. Thank you for replying - I didn't even know if my engine is a direct injection or indirect injection system. If it's indirect injection what you said seems plausible.

Your 617.912 is an indirect injection engine.

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if the injector for that cylinder is very leaky you may end up with lots of diesel fuel in your engine oil.not a good thing!

How can you know if you have a leaky injector?

Mine only "beats" like a small hammer when it's cold or when I lug the engine, otherwise it operates normally.

Take yolur injectors (all of them) to a Diesel injection shop and have them tested for the right spray pattern. They can also test for leaks. Properly working injectors are the most important part in making your car run well. If they leak or 'dribble' this can dilute your engine oil. This can also wash the oil off your cylinder wall and cause premature wear to that cylinder.

Is there any way I can check if the injectors is leaking into the engine oil?

Oil analysis is the only real method to test for fuel in your oil. A rough test is to put a few drops of oil on a piece of paper. If there is any fuel dilution in the oil after a while you will see a light colored ring around the outside of the oil sample. This ring is the fuel being drawn away from the thicker oil. Do this test when the oil is hot.