All coins that were on the quark chain will be swapped 1 for 1. The X11 chain is a whole new blockchain with a premine to cover everyones coins. The coins not swapped will be burned. So currently all the coins on Bittrex and Mymue are being counted and swapped. From there the chain will go public for all to mine and to start personal masternodes etc.
The team are doing this as openly as possible and as always the block explorer will show people everything as well and you will be able to see that nothing is being hidden.