Whenever I start up my Mac I need to fill in the password to my user account and it shows this ugly low-res user picture stretched out as my user account picture in the login screen. After being logged in and Filevault on my Mac is unlocked, returning to the login screen shows the regular high-res user picture. My question being: Where is that low-res cached user picture located, how do I reach it, and would it be possible to replace it by a high-res image, and if so how?
When you boot up your Mac, it starts from a non-encrypted part of the disk that only contains a very limited subset of macOS. Basically it can display that login screen and that's it. The pictures displayed are "hardcoded" into it - so it is not loading those account pictures like usual.
As soon as you have logged in, the ordinary disk can be unlocked (i.e. decrypted) - and then the full macOS system takes over - and now your account pictures are loaded from the file system like usual.
If there's a problem with the account picture during the first part of the boot, I would suggest simply trying to change the account picture. When you do that, the information in that non-encrypted part of the disk is updated. You can check by rebooting and seeing the new picture. Afterwards you can change it back to the original picture you want, and the login window information will be regenerated - this time hopefully without any flaws.