Avoiding stripping of HTML in Custom Taxonomy Meta Field

you can use esc_attr

function save_taxonomy_custom_meta_bandcamp_embed_music( $term_id ) {
    if ( isset( $_POST['term_meta'] ) ) {
        $t_id = $term_id;
        $term_meta = get_option( "taxonomy_$t_id" );
        $cat_keys = array_keys( $_POST['term_meta'] );
        foreach ( $cat_keys as $key ) {
            if ( isset ( $_POST['term_meta'][$key] ) ) {
                $term_meta[$key] = esc_attr( $_POST['term_meta'][$key] ); // encoded text with HTML entities
            }
        }
        // Save the option array.
        update_option( "taxonomy_$t_id", $term_meta );
    }
}  
add_action( 'edited_hhie_artists', 'save_taxonomy_custom_meta_bandcamp_embed_music', 10, 2 );  
add_action( 'create_hhie_artists', 'save_taxonomy_custom_meta_bandcamp_embed_music', 10, 2 );