Share your experience!
The top plastic edge (the piece surrounding the headphone jack and all across the top) of my XZ1 has fallen off and shows some signs of deformity. Purchased the phone used and so do not know what misuse it has been subjected to. I´ve tried to find this part on-line, but to no avail. Any tips as to where this part can be obtained and how it can be reattached would be greatly appreciated.
I'm sorry to hear that, but you can't buy that part on it's on, you have to get the whole Xperia XZ1 "housing"
Hi @PWF, sorry to hear about this. 
Do I understand correctly that it's the top part of the "frame" that is deformed? As far as I know and as @uliwooly mentioned you can't only purchase this spare part on it own, however since I don't work with repairs and don't have any kind of education about this due to all repairs being made by our service partners, it's hard for me to give you a detailed answer.
You can of course have a look at some kind of tear down video, but I think it's connected to the frame somehow and the entire frame/housing will need to be replaced.
I hope that helps a bit!
Thanks for your answers, now the big question is: where can I purchase the complete housing and all the adhesive tapes needed to repair the phone back to a proper and whole physical condition. Any and all links would be greatly appreciated.
Check amazon and/or ebay
here is a tutorial
https://www.ifixit.com/Device/Sony_Xperia_XZ1
make sure to buy the double sided tapes
Thanks for the tips, they were the first I tried, but to no avail. Several firms selling some spare parts, but I haven´t found the complete back casing anywhere :(.
Hi again @PWF,
Yeah, it's probably quite easy to find charging port, display, back cover and so on but the entire casing may be a bit harder to get a hold of.
The last option is so send the device to an authorized service centre, but this will of course be more expensive than fixing it on your own.
Yes, my findings as well, unfortunately the costs would be so expensive that I´m afraid that I´ll be forced to live with the problem.
@PWF1, yeah.
If you still have the part laying around, perhaps you can try and fit it in place and then use some kind of cover that goes "over" the top part of the frame to keep it in place.
Most TPU cases only cover the sides though and not the top and bottom. 
I hope that you find some kind of solution at least and have a nice weekend! 