You have no control over what you get. You are extremely recommended to play until you are asked to start a chain. Otherwise, the last chain you were asked to respond to will be left in limbo while you do other stuff.
Seriously, it's a stupid thing I think the maker is fixing. If you stop playing, you're still attributed to that Doodle you didn't respond. Therefore, no one else can add to it, and you look like a HUGE ass by suddenly halting the chain.