I didn't test this, but I think what you want is:

$infile="hosts.txt";
open(INPUT, $infile) || die "Error opening $infile\n";
my @allhosts = <INPUT>;
close INPUT;
while ($approvhost=<STDIN>) 
    {
    chop($approvedhost); # or it won't partially match 
                         # your hosts entries becaus of 
                         # the training \n
    unless ($approvedhost) { last; } # so you can quit 
                                     # with a null entry
    foreach $host (@allhosts) # omit the <> you're not
                              # reading a file or stdin
        {
        if ($host =~ m/^$approvhost/)
            {
            print $host;
            }
        }
    }
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