how to use tax_query to apply both terms or one if one is empty

Question

Change your code with the following:

$args = array(
  'post_type' => 'property',
  'posts_per_page' => 5000,
);

$statuses = explode( ',', $st_term_final_string);
$terms = explode( ',', $il_term_final_string );

if ( $statuses || $terms ) {
  $args['tax_query'] = array();
  if ( $statuses ) {
    $args['tax_query'][] = array(
      'taxonomy' => 'Status',
      'field' => 'slug',
      'terms' => $statuses
    );
  }

  if ( $terms ) {
   $args['tax_query'][] = array(
     'taxonomy' => 'County',
     'field' => 'slug',
     'terms' => $terms
    );
  }

  if ( $statuses && $terms ) $args['tax_query']['relation'] = 'AND';

  $loop = new WP_Query( $args );

  // do your stuff here

} else {

  // You have no statuses nor county, I don't know what you want to do in this case

}

Hope it helps.