All contacts are stored in Androids contacts storage provider. If the sync did not run properly and your contacts storage is corrupt you can’t get your contacts back. I suggest to maybe look in the SQlite database directly. If you’ve a rooted phone as it seems you can access it also via adb. Look at our FAQ at point 3 and 4:
Maybe you can copy them from there or at least save it.
Also have a look here for a better understanding of the components involved with DAVdroid:
https://www.davdroid.com/faq/system-integration/ It always helps 🙂