Because you haven't emptied the pipe, which means that tasklist is blocked waiting to finish writing to it.

Just closing the pipe won't allow tasklist to end; the pipe won't close until it does. Deadlock.

The answer is to empty the pipe before closing it:

use strict;
use warnings;

use IO::Pipe;
my $cmd = "tasklist";

my $pipe = IO::Pipe->new();
$pipe->reader($cmd);

while (my $line = $pipe->getline()) {
    print $line;
    last if $line =~ /^smss/;
}

1 while $pipe->getline;

$pipe->close();
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