Hmmmm
Personally, I think the best solution is that if you type /leave in certain minigames that it costs you either a fixed amount, lets say €50,000 that go's to the winner/last person or all of your money you have in your pocket at the time if you have more than 50k
Lets face it, deciding to commit to a game by joining it and then being a dick and /leave 'ing when you're losing isn't excatly fair, so a small bit of punishment and a notifcation in the chatbox that 'X has no balls and left /brief' would encourage more people to play.
In the /brief game however, if your car is destroyed its kinda pointless staying in the game, so I can understand why people /leave then. When what happens if the person with the briefcase car is destroyed and has to run half way accross the map... ? this takes too long. Can the game be changed so that when your car (a sultan I believe) destroyed a bmx or a very crap car spawns for you? Least then you're not totally out of the hunt and would probably speed up the game.
Maybe give each player 3 cars. They start off in a fast, yet weak car with not so great handling, lets say the cheetah, then maybe if that gets destroyed you get a mid range car, such as the sultan then maybe for the 3rd a bmx or vortex.
Actually even just having one replacement and that being a vortex would be the best, slow and if you crash into water having a normal car spawn would be pointless as it would spawn in the water, but sinc the vortex is also a boat it would solve the problem.