open my $fh, "<", $file or warn "Couldn't open '$file': $!" and exit;

##</code><code>##

my $file = "does-not-exist";

while (<STDIN>) {
    eval {
        open my $fh, "<", $file
            or warn "Couldn't open '$file': $!" and exit;
    };
    print STDERR "ERROR: $@" if $@;
}

##</code><code>##

while (<STDIN>) {
    eval {
        open my $fh, "<", $file
            or CORE::die "Couldn't open '$file': $!";
    };
    print STDERR "ERROR: $@" if $@;
}

##</code><code>##

ERROR: Couldn't open 'does-not-exist': No such file or directory at ./680735.pl line 10, <STDIN> line 1.

ERROR: Couldn't open 'does-not-exist': No such file or directory at ./680735.pl line 10, <STDIN> line 2.
...