Where do you increment $a_counter?

This is how you can fix it:

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dumper;


my @left_split = ('stuff', '', 'stuff', '', '10', '', '-', '');
my $index = 0;
while ($index <= $#left_split) {
    if ('' eq $left_split[$index]) {
        splice @left_split, $index, 1;
    } else {
        ++$index;
    }
}
print Dumper \@left_split;
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But I would simply use grep:

@left_split = grep '' ne $_, @left_split;
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