Perl - Calling subclass constructor from superclass (OO)

In general it's a mistake (design-wise, not syntax-wise) for the new method to return anything but a new object. If you want to sometimes return an existing object, call that method something else, e.g. new_from_cache().

I also find it odd that you're splitting up this functionality (constructing a new object, and returning an existing one) not just into separate namespaces, but also different objects. So in general, you're closer with your second approach, but you can still have the main constructor (new) handle a variety of arguments:

package Foos;
use strict;
use warnings;

sub new
{
    my ($class, %args) = @_;

    if ($args{name})
    {
        # handle the name => value option
    }

    if ($args{some_other_option})
    {
        # ...
    }

    my $this = {
        # fill in any fields you need...
    };

    return bless $this, $class;
}

sub new_from_cache
{
    my ($class, %args) = @_;

    # check if the object already exists...

    # if not, create a new object
    return $class->new(%args);
}

Note: I don't want to complicate things while you're still learning, but you may also want to look at Moose, which takes care of a lot of the gory details of construction for you, and the definition of attributes and their accessors.

It is generally speaking a bad idea for a superclass to know about its subclasses, a principle which extends to construction.[1] If you need to decide at runtime what kind of object to create (and you do), create a fourth class to have just that job. This is one kind of "factory".

Having said that in answer to your nominal question, your problem as described does not seem to call for subclassing. In particular, you apparently are going to be treating the different classes of Foos differently depending on which concrete class they belong to. All you're really asking for is a unified way to instantiate two separate classes of objects.

So how's this suggestion[3]: Make Foos::Exists and Foos::Pending two separate and unrelated classes and provide (in Foos) a method that returns the appropriate one. Don't call it new; you're not making a new Foos.

If you want to unify the interfaces so that clients don't have to know which kind they're talking about, then we can talk subclassing (or better yet, delegation to a lazily-created and -updated Foos::Handle).

[1]: Explaining why this is true is a subject hefty enough for a book[2], but the short answer is that it creates a dependency cycle between the subclass (which depends on its superclass by definition) and the superclass (which is being made to depend on its subclass by a poor design decision).
[2]: Lakos, John. (1996). Large-scale C++ Software Design. Addison-Wesley.
[3]: Not a recommendation, since I can't get a good enough handle on your requirements to be sure I'm not shooting fish in a dark ocean.

It is also a factory pattern (bad in Perl) if the object's constructor will return an instance blessed into more than one package.

I would create something like this. If the names exists than is_created is set to 1, otherwise it is set to 0.. I would merge the ::Pending, and ::Existing together, and if the object isn't created just put that into the default for the _object, the check happens lazily. Also, Foo->delete() and Foo->change() will defer to the instance in _object.

package Foo;
use Moose;

has 'name' => ( is => 'ro', isa => 'Str', required => 1 );
has 'is_created' => (
    is => 'ro'
    , isa => 'Bool'
    , init_arg => undef
    , default => sub {
        stuff_if_exists ? 1 : 0
    }
);

has '_object' => (
    isa => 'Object'
    , is => 'ro'
    , lazy => 1
    , init_arg => undef
    , default => sub {
        my $self = shift;
        $self->is_created
            ? Foo->new
            : Bar->new
    }
    , handles => [qw/delete change/]
);