Perhaps if you searched for “outdated tetracycline” or “tetracycline renal problems” you’d get some more information on the whole expired doxy issue- but most of the random Medical sites I saw just seem to point out that expired tetracycline is toxic to the kidneys.
As to how it actually breaks down, I can’t really answer that question- but if you are asking is there a known side effect of outdated tetracyclines- then yes, renal impairment, necrosis, and failure are all possible with outdated tetracyclines.
Wiki on Fanconi, drugs.com on Tetracycline, tetracycline precautions, and one more on the side effects of Doxycycline All of these point out that yes, Outdated Tetracyclines seem to be bad for your kidneys.
And one quote to boot, since it was the best summary I could find on expired Doxy:
Sorry I couldn’t answer your initial question, but I hope I can at least help you reaffirm that yes, outdated Doxy/Tetracyclines can do some bad things (and ergo, must probably break down or at least have something unique about them that this medication is quite explicitly labeled with causing a certain specific set of problems once it’s expired).