See kill and getppid. Here's a recipe:

#!/usr/bin/perl

print "process $$ started\n";
if ((my $pid = fork) == 0) {
    my $ppid = getppid;
    while (1) {
        sleep 1;
        unless (kill 0, $ppid) {
            print "child: parent($ppid) gone, exiting.\n";
            exit;
        } else {
            print "child: parent($ppid) still alive...\n";
        }
    }
} else {
    my $secs = int rand 20;
    print "parent: sleeping $secs seconds\n";
    sleep $secs;
}
print "parent: exiting after 1 second\n";
sleep 1;
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