Get rid of the whitespace surrounding your IN filehandle. Change: 
while ( < IN > ){

[download]

To: 

while ( <IN> ){

[download]

B::Deparse can shine a little more light upon the situation (Tip #6 from the Basic debugging checklist): 

perl -MO=Deparse 867882.pl

my $dir = 'input_files';
die "can't opendir $!" unless opendir DIR, $dir;
while (defined(my $file = readdir DIR)) {
    do {
        print "The directory and file are $dir/$file\n";
        die "Can't open input file $!" unless open IN, "< $dir/$file";
        use File::Glob ();
        while (defined($_ = glob(' IN '))) {
            print $_;
        }
    };
}
closedir DIR;

[download]

Here is an explanation from perlop:

Even <$x > (note the extra space) is treated as glob("$x ") , not readline($x).

In reply to Re: reading files from a directory by toolic
in thread reading files from a directory by kevyt

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.