Thank you, but I couldn't really find anything there either.
Fortunately, a friend of mine looked into the code and found an undocumented method socket() which returns the socket used.
So in case someone else has got troubles with buggy LDAP servers:
my $ldap = Net::LDAP->new(...)
....
$ldap->unbind()
my $socket = $ldap->socket();
close $socket if $socket;