As one who has worked in a lot of places with lots of personal coming and going all the time, I too have noticed that phenomenon. There have been many, many reliable and valuable people among them, (hopefully even me), at times but they have all been replaced, with someone who has always managed to do the job adequately, if not sometimes even better!
So it never pays to become proud and boast that you can’t be replaced because you can and your boasting may just be the cause of you being replaced. "Just to prove you wrong”.
So if you are really among that somewhat rather elite group, be happy but don’t be proud, otherwise you just might pull your arm out of the bucket and show the world your true worth, hey?
So if you think you might be indispensable, don’t boast about it but help others, as to the best of your ability and show, not tell, but show, them, just how valuable you really are.
Remember you are not even thought indispensable when you think you are, but only when everyone else there thinks you are. Till then, your pride makes you vulnerable and maybe even dispensable, rather than indispensable.So in closing, if you really think you are indispensable don’t tell anyone but show everyone and not just your superiors either.