I wrote PerlX::Maybe precisely for this purpose!

use v5.14;
use strict;
use warnings;

use PerlX::Maybe;

package Foo {
    use Moose;
    has foo => (is => 'ro', default => 'whatever');
}

my $value = 'hello';
print Foo->new(maybe foo => $value)->dump;

$value = undef;
print Foo->new(maybe foo => $value)->dump;
[download]

As you can see, the maybe keyword is applied at the "consumer side" - i.e. in the code that is using the class.

Within the class itself, you could try MooseX::UndefTolerant though that has a major caveat listed in the documentation!