Without entering in the matter of checking linux users (you got already authoritative suggestions) I'd like to point you to some general perl modern practices:

• I dont see strict nor warnings in use.. this must be a mantra in all your programs
  
  
• open(FILE, $filename) or die.. is correct but we dont use bareword filehandles since years: open(my $file_handle, $filename) or die .. is the idiomatic (idiomatic perl => good thing) form (see Is there a problem with using barewords as filehandles ?).
  
  
• update you use the implicit opening mode! Please join us in the use of 4 arguments open like in open(my $fh, "<", "input.txt") Explicit -> more readable -> better
  
  
• as already said you chomp $username in the wrong place: the right place is just after my $username = <STDIN>; (I added my to your line ;)
  
  
• you (at least as presente here) use a poor indentation: you close 3 braces at the same level of indentation while they are not at the same level. See Perl::Tidy for a code beautifier, then it will be by heart
  
  
• if A eq B .. if A ne B is logically wrong. if .... else... is what you want. Or in more complex cases if .. elsif .. else
  
  
• while dealing with user inputs a typical error is to overlook what you got: I find useful, presenting something to the screen, to enclose these kind of things inside square brackets, like: print "User: [$username] does not exist.\n"; These brackets does not interefere with your output even in case of other brackets, like in: print "Home directory: [$fields[5]]\n";
  
  
• as already said @array[0] is an array slice, so it is an array and $array[0] is the first element of the array, so a scalar.