Typing "cable burn in" into google brings up various oppinions.....
So I did. What you get are loads of forum entries with the revolving debates that we keep on getting here. There are also a surprising amount of companies that offer cable burning in services and equipment. There is very little science. You do get a lot of opinion written in a scientific style using scientific words. But it is easy to see that such is theoretical, is based on assumptions and continually slips into philosophical analogy and reasoning, but is presented as science. That is from both camps.
So in the end, some people hear a difference to cables over time and others do not. As to why that is, not sure and I don't think that anyone truely is.
From me, for what it is worth, I have heard one cable, the Kimber 4TC speaker cable change over time. The change was not significant and it did not really sound better. It just sounded different, but not in a bad way. As for all of the other cables I have owned, nothing.
IMHO, rather than going round and round again, much to the delight of certain mischief makers, I will only contribute to cable threads where something new, positive, interesting and hopefully scientific appears.