Leaving hundreds of filehandles open is probably a bad idea. I'm assuming that you're leaving them open in order to read them line-by-line. However, there are more scalable ways of doing that.

You can get the current position of the file read buffer with:

my $file_pos = tell($fh);
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And you can go to that file position with:

seek($fh, $file_pos, 0);
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If you keep track of your position in each file, you can open one file at a time and still read through hundreds of files line-by-line. For example, here's a code snippet that reads through and prints out a cross-section of a bunch of different files, but still only opens one file at a time:

#!env perl

use strict;
use warnings;

our @Files = @ARGV;

MAIN: {

    # A table storing each active filename and its
    # current position
    my %file_table = ();

    # Line number for each file we're reading through
    # (for printout purposes only)
    my $line_num = 0;

    # Set up our file table to point everything to 0
    foreach my $file (@Files) {
        $file_table{$file} = 0;
    }

    # Keep printing each line so long as at least one file
    # has stuff to print
    while ( scalar keys %file_table ) {

        # Keep track of line numbers
        $line_num++;

        # Open each file, seek to last read position,
        # read a line, then note the next position
        foreach my $file ( sort keys %file_table ) {
            open( my $fh, '<', $file ) or die "Oops! $!";
            seek( $fh, $file_table{$file}, 0 );
            my $line = <$fh>;
            print "$file\t$line_num\t$line\n";
            if ( eof $fh ) {
                delete $file_table{$file};
            } else {
                $file_table{$file} = tell($fh);
            }
            close($fh);
        }

    }

    print "All done\n";

}
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