This isn't quite you had in mind, but not only did I find a case where <> returns an empty string, it does so before the last "line".

>perl -MData::Dumper -e"while (<{,0,a}>) { print Dumper $_ }"
$VAR1 = '';
$VAR1 = '0';
$VAR1 = 'a';
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A tied handle could do it too, say one that autochomps.