You make it sound like Perl launches a thread to fill the buffer

That's not what I meant.  Perl tries to fill the buffer whenever it's empty and something is attempting to read from it — which in this case is the eof, as you note.

        sub process_scheme{
          my ($output_file) = @_;
          open (OUTPUT_FILE, ">", $output_file) || die "cannot open lo
+g file";
          my $scheme_pid = open (WORKER, "worker_program < $input |") 
               || die "cannot pipe worker";
          my $str;
          while (1) {
              eval{
                  local $SIG{ALRM} = sub { die "alarm\n" }; # NB: \n r
+equired
                  alarm 1;
                  if (eof(WORKER)){    
                      close WORKER;
                      close OUTPUT;
                      return 1;
                  }

                  $str = <WORKER>;
                  alarm 0; # if this line is removed, the signal is ca
+ught, but outside of eval, so it halts the script
              };
              if ($@) {
                  close OUTPUT_FILE;
                  close WORKER;
                  return 0;
              }

              # process the line
              #  some code ...
              # print the line to log
              print OUTPUT_FILE $str;
          }
      }
[download]

but it still does not work

What doesn't work?

The timeout works fine. I changed

my $scheme_pid = open (WORKER, "worker_program < $input |")
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to

my $scheme_pid = open (WORKER, "-|", $^X, '-e', '$|=1; for (1..100) { 
+print "%d\n", $_*$t; sleep(2) }')
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and the timeout triggered. The log file contained only "0".

You'll need to fix the return 1, though. That will only return out of the eval, not out of the sub.

It still stuck, not alarmed for some reasons. My code right now has become:

sub process_scheme{
    my ($output_file) = @_;
    open (OUTPUT_FILE, ">", $output_file) || die "cannot open log file
+";
    my $scheme_pid = open (SCHEME, "./t.pl | ") || die "cannot pipe sc
+heme";
    my $str = "";
  MAIN:
    while (1) {
        eval{
            local $SIG{ALRM} = sub { die "alarm\n" }; # NB: \n require
+d
            alarm 5;#$allow_time;
            if (eof(SCHEME)){    
                close OUTPUT_FILE; close SCHEME;
                last MAIN;
            }
            $str = <SCHEME>;
            alarm 0;
        };
        if ($@) {
            close OUTPUT_FILE;
            kill $scheme_pid;
            close SCHEME;
            return -$current_player;
        }

        # process the line
        print OUTPUT_FILE $str;
    }
    return 1;
}
[download]

where the t.pl is

while(1){};
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The script gets stuck, waiting forever, not stopping/returning anything