The problem came up recently about how to make sure plugins activated in the WordPress plugin UI don’t get deactivated if they are necessary for a site to function.  I thought that was an interesting thought puzzle worth spending 15 minutes on, so I came up with this function as a solution:

function dt_force_plugin_active( $plugin ) {
	add_filter( 'pre_update_option_active_plugins', function ( $active_plugins ) use ( $plugin ) {
		// Match if properly named: wp-plugin (wp-plugin/wp-plugin.php).
		$proper_plugin_name = $plugin . '/' . $plugin . '.php';

		if (
			file_exists( WP_PLUGIN_DIR . '/' . $proper_plugin_name )
			&& is_file( WP_PLUGIN_DIR . '/' . $proper_plugin_name )
			&& ! in_array( $proper_plugin_name, $active_plugins, true )
		) {
			$active_plugins[] = $proper_plugin_name;
			return array_unique( $active_plugins );
		}

		// Match if improperly named: wp-plugin/cool-plugin.php.
		if (
			file_exists( WP_PLUGIN_DIR . '/' . $plugin )
			&& is_file( WP_PLUGIN_DIR . '/' . $plugin )
			&& ! in_array( $plugin, $active_plugins, true )
		) {
			$active_plugins[] = $plugin;
			return array_unique( $active_plugins );
		}

		return array_unique( $active_plugins );
	}, 1000, 1 );
}

Which can be activated in your theme’s functions.php like so:

dt_force_plugin_active( 'akismet' ); or dt_force_plugin_active( 'wordpress-seo/wp-seo.php' );

The only downside that I’ve seen so far is that you still get the Plugin deactivated. message in the admin notices.