... I suppose you might be able to do something similar...

I haven't used it, but Expect says, for $object->expect($timeout, @match_patterns), "If $timeout is undef Expect will wait forever for a pattern to match". That indicates your supposition is right.

If you want to wait longer, but not forever, you can just set the $timeout accordingly... and maybe use $object->restart_timeout_upon_receive(1), which appears re-start the timer every time new data arrives (so if the command is outputting a word every 15 seconds, and can be considered dead if it goes more than 30 seconds, and the word you're looking for is the fifth word, then you could use a timeout of 30 seconds with the ->restart_timeout_upon_receive(1), and it should ... ah, enough of this "should" stuff:

#!/usr/bin/env perl -l
use warnings;
use strict;
use Expect;


foreach my $restart (0, 1) {
    my $exp = Expect->new();
    $exp->restart_timeout_upon_receive($restart);

    $exp->spawn(qw{perl -le 'foreach(@ARGV) { print $_; sleep 2; } ' w
+ait until seeing the fifth word })
        or die "cannot spawn: $!\n";

    my @return = $exp->expect(4, 'fifth');
    print "restart=$restart -> \@return = ", join ', ', map { $_ // '<
+undef>' } @return;
}
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Yep, that timedout on the first run, but continued through to the 'fifth' on the second run.