eval{<$arg>} was my third thought. But testing reminded me that <...> doesn't give you any reasonable way to distinguish "end of file" from "error reading".

I don't understand how eval could be employed since the following program does not die when you read from <$fh>:

my $fh = 'f.tmp';
my $s = <$fh>;
print "i am here: s='$s'\n";
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That is, there is nothing to catch.