Or something that wouldn't be considered buggy:

package Logger;

our $default_logger = __PACKAGE__->new();

sub new {
  my $this = bless {};
}

sub DESTROY {
  print "DESTROY\n";
}


package MAIN;

END {
  print "END\n";
}
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or

package Logger;

my $default_logger = __PACKAGE__->new();

sub new {
  my $this = bless {};
}

sub log {
   $default_logger->foo();
}

sub DESTROY {
  print "DESTROY\n";
}


package MAIN;

END {
  print "END\n";
}
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In both cases, a package variable ($Logger::default_logger in the first snippet, &Logger::log in the second snippet) keep the object alive until global destruction (where package variables are destroyed).