Data not being saved in multi-checkbox custom field

@norbertk

Yes, if you don’t update the meta_values when there are no selected options
the old values will be displayed.

foreach( $names as $name ) {        
        if ( isset( $_POST[$name] ) && ! empty( $_POST[$name] )) {
            $submitted = array_map( 'sanitize_text_field', $_POST[$name] );
            update_user_meta( $user_id, $name, $submitted );
        } else {
            update_user_meta( $user_id, $name, array() );
        }
    }

Thank you, that worked!