Okay this version finds the ends of the paths, then builds them backwards from their. As long as the data is good it will run fine ;) I added the pair (1,2) which breaks the above code.

#!/usr/bin/perl
use strict;
use warnings;

use Data::Dumper;

my $pairs = {
    (4,-1),
    (2,6),
    (6,4),
    (1,2),
    (3,5),
    (5,-1),
    (99,-1),
};


my @paths;


#get the ends of all the chains
#then the next pieces, and so on, until all pairs are used.

for my $key ( grep { $pairs->{$_} == -1 } keys %$pairs ) {
    push @paths, [$key, -1];
    delete $pairs->{$key};
}

while ( keys %$pairs ) {
    for my $path ( @paths ) {
        for my $key ( keys %$pairs ) {
            if ($pairs->{$key} eq @$path[0]) {
                unshift @$path, $key;
                delete $pairs->{$key};
            }
        }
    }
}

my $hh;
for my $path (@paths) {
    my $temp = pop @$path;
    my $key  = shift @$path;
    for (reverse @$path) {
        my $t = {$_ => $temp};
        $temp = $t;
    }
    $hh->{$key} = $temp;
}
print Dumper($hh);
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