# 1. elide manually managed count variable
# 2. read current line into an actual variable
while(my $line = <$fh_bigfile>) {
  # 3. let perl manage the count variable
  for my $i (0..$#inputs) {
    # 4. wrong sigil, use $...[$i] instead of @...[$i]
    # 5. explicitely refer to the line to print it
    # 6. enclose file handle in braces to make it more obvious
    print {$filehandles[$i]} $line
      if (/$regex[$i]/../^END_OF_BLOCK/);
  }
}