Much better to use chomp which only removes EOL character(s):

As say the docs:

This safer version of chop removes any trailing string that corresponds to the current value of $/ (also known as $INPUT_RECORD_SEPARATOR in the English module). It returns the total number of characters removed from all its arguments. It's often used to remove the newline from the end of an input record when you're worried that the final record may be missing its newline.

> cat last_assignee.txt
john
> ./684200.pl
In while loop
john
> cat 684200.pl
#!/usr/bin/env perl

#use warnings;
#use strict;

open( last_assignee, '<', "last_assignee.txt" ) or die "Unable to open
+ last_assignee.txt for READ\n";

# Get the last assigned value and store it to a variable
while (<last_assignee>) {
    print "In while loop\n";
    print $_;
    chop;
    if ( $_ ne "" ) {
        $assignee_last = $_;
    }
}
[download]

Are you sure your input file has anything in it?

I intentionally commented out use warnings; use strict; just to try to duplicate your results. Make sure you use these in your code.

yes I do have values. I think it is just a new line that was needed after the first line. I added a new line and it is working. I update this file in the script so I was just putting in the value and for some reason it did not like it.

$_ = <last_assignee>;
chomp;
if ($_ ne "") {
    $assignee_last = $_;
}
[download]

As others have suggested, make sure you add strict and warnings, and use chomp rather than chop.

Finally, a question: Your if and the assignment to $assignee_last looks to me like a red flag, but it's hard to tell without seeing what follows. What does your program go on to do if $_ eq ""?