There are dedicated servers, the only way you would get kicked out of a game because of the "host" leaving, would be if his internet went down and he was the one actually keeping the server up. Steam is going to offer a free dedicated stand-alone server tool. And of course for the people that don't have the internet speed to run their own server, places that sell servers for games like CS:S will also be selling these servers. I guess it comes down to what platform you're playing on too, you should mention that for a topic like this.
http://bethblog.com/index.php/2011/04/28/brink-dedicated-server-faq/
Not to be rude, but you should read the entire post, I clearly said that they are for the PC and that for a question like this he needed to specify which system it's on, but thank you for stating the obvious
Really? Where did you say that? The closest you come to saying "PC" is "Steam is going to offer a free dedicated stand-alone server tool." Which isn't clearly saying it, and doesn't actually exclude consoles.