Well, you could come up with a hackish work around by caching the value of $$ when you open your pipe, and then check to see if the value is equivalent when you close it to decide if the error should be propagated or not, e.g.

my $status = $pipe->close;
die $! if $$ != $mainpid;
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If you are confident that only the parent thread will access the output methods, you could write the above more like:

if ($$ == $mainpid) {
    $pipe->close or die $!;
}
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Both of these solutions require you to put the effort into handling the issue, which is less aesthetically pleasing to me, but gets the job done. I cannot come up with an effective way of propagating real errors and blocking apparent errors from the fork that seems elegant.

The only other possibility that occurs to me is to check if the pipe process is a child of the current process before error propagation (as opposed to caching pid), but this does not strike me as fundamentally cleaner.