Thanks for the reply. Here is what I've done to find existing files that are corrupted:
grep -rL "</fingerprint>" $JENKINS_HOME/fingerprints
I found two files, one of them empty, the other one indeed corrupted (not written to the end), so I deleted both. This didn't solve the issue.
I restarted Jenkins, still no luck.
Then I was digging down into where exactly the issue was occurring. I found that multiple withCredential blocks with different credentials were failing with above exception. As I didn't know where else the fingerprint could be stored I simply updated that credentials and now builds are working again.