any moving part will change over time, quality ones will settle rapidly into a stable system and last long that way.
the pads on the headphone definitely change the sound and change themselves over times(losing elasticity, taking in the shape of the head, letting the driver closer to the ear....).
so like everything physical in the world, time has an impact on it.
now perhaps more relevant questions:
how comes audiophiles always think it's an improvement?
what are the real magnitudes of changes? how do they compare to simply taking the headphone off and putting it back on the head?
do we know of a method to make the "burn in" process end up with better sound? has it been measured by anybody?
are the people who talk about how things improved, considering that human senses constantly recalibrate themselves to the new experiences?
my personal quest to answering those questions led me to believe that most of people's feedback on burn in are BS pure and simple. if only because they don't have a clue how to test anything properly and as such do not have the right to a claim. yes changes occur, anytime I tried to measure it, it ended up being smaller than the way I put the headphone on my head, smaller than the difference between 2 pairs of the same headphone, and smaller than the difference between left and right driver. it has to me, been an irrelevant quantity of change and I have seen nothing to say that I could control it so I do not have a burn in ritual.
after a real long time and great many hours of use, any damping filter becomes dirty and as a result acts like a higher value damper. it's very obvious with IEM filters. between ear wax, dust, human skin, etc. and them being so small, you are guaranteed to notice an attenuation of the resonance freq, along with an attenuation of mid-trebles area. IDK if that should be called burn in, like IDK if the pads giving in over time should be called burn in. what I know is that after changing both with new ones, the sound goes uncannily back to what it was when new(I mean measured, not putting a wet finger in the air and decide I am able to tell how something sounded 1year ago by ear).