Don't wield symbolic references for this purpose. You don't need them here. Use strict to disabuse yourself of any temptation. Why it's stupid to use a variable as a variable name.

In your code above, ${'a'} is a symbolic reference to a package global named $main::a. And ${a} is synonymous with $a, which in the scope you're using it in, refers to the lexical version of $a, not the package global.

Instead, either use real references, or a hash:

# Using hard references
my @cat = (1,2,3);
my @dog = (5,6);
my @pig = (4,3,2,1);
for my $array (\@cat, \@dog, \@pig) {
    # On first iteration $array will contain a reference to @cat.
    # On second iteration, $array will contain a reference to @dog.
    # On third iteration $array will contain a reference to @pig.
}
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...or do this...

# Using a hash
my %animals = (
    cat => [1,2,3],
    dog => [5,6],
    pig => [4,3,2,1],
);
for my $animal_type (keys %animals) {
    my @values = @{$animals{$animal_type}};
    # Animals will come in an unpredictable order, but as an example:
    #    First iteration, dog will be handled.
    #    Second iteration, pig will be handled.
    #    Third iteration, cat will be handled.
}
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