Get all posts WHERE custom_field is LIKE value

You can use meta_query in WP_Query

$args = array(
    'post_type' => 'post',
    'meta_query' => array(
        array(
            'key' => 'subject',
            'value' => 'Subject Two',
            'compare' => 'LIKE'
        )
    )
 );
$query = new WP_Query( $args );