As you say, programming like this probably causes some maintenance problems. Having said that, you should look at UNIVERSAL::isa()

Your test of $invokant also won't work if called by a class inheriting from MyClass:

package MyClass;

sub new
{
  print shift;
}

package MySubClass;
@MySubClass::ISA =  qw(MyClass);

package main

my $test = new MySubClass;

__DATA__
prints "MySubClass"
[download]

So having said that, I probably would write the constructor like this:

sub _new_or_old
{
  my $invokant = shift;
  defined( $invokant ) or return undef;

  if( UNIVERSAL::isa($invokant, 'MyClass' )
  {
      return $invokant;
  } else {
      my $self = {};
      bless( $self, $invokant );
      return $self;
  }
}
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