imaplogin: malloc: Input/output error

Today I received lots of this error messages on one of my mailservers.
Google wasn't as helpful as usual, but after searching for a long while I found the solution and want to provide it here so that the next time googling for this issue won't take that long again.

imaplogin is part of the courier-imap(-ssl) suite so this issue may only be relevant for those who use courier to provide IMAP to your users.

After checking all parts of the courier suite, the authentication mechanism and some other stuff the problem still hasn't gone away.
The only thing that helped was restarting the FAM daemon which suddenly stopped working as it seems.