BackupPC crashes on start

When installing BackupPC on a fresh Alpine installation, the daemon crashes immediately on startup with an error:
unix bind() failed: No such file or directory

Steps to reproduce:
Install Alpine version 3.5 or newer
Install BackupPC - apk add backuppc
Start BackupPC - rc-service backuppc start

It will start successfully but crash immediately. The aforementioned error is in /var/log/BackupPC/LOG. The /run/BackupPC directory is created successfully and has the correct permissions.

The package works in 3.4 and 3.3, I did not test earlier versions than that.

Installing the version of BackupPC from 3.4 on 3.7 works after patching /usr/lib/BackupPC/lib/BackupPC/Lib.pm to fix a deprecated syntax error (Ubuntu patch for the same issue: https://launchpadlibrarian.net/253993785/lp1570987.debdiff).

(from redmine: issue id 8368, created on 2018-01-01)