Hi Stoyan,
Does the system that BackupPC fails to start on have ldap configured?
I have this problem too and was looking at it again following your email, I noticed from strace that a called was being made to .ldaprc during backuppc startup.
I have removed all ldap config and packages from the server and backuppc now starts correctly.
I know this isn't a fix but at least it's a step forward.
I removed libnss-ldap auth-client-config ldap-auth-config ldap-auth-client libpam-ldap
I reran pam-auth-config and disabled the auto creation of home-dirs and systemd registration that I had enabled for ldap support.