What happens when the EOS tokens become unfrozen? Will trading continue after June 14th?
This is just an inital state while the blockchain is booting. The ERC20-Tokens are just representative for the final EOS-Tokens.
The potential blockproducers verify the distribution snapshot of that tokens and map them to an EOS adress instead of an Ethereum adress. They are frozen till the public release, because trading them would result in more inconsistencies and make everything more complicated.
After all potential blockproducers/testers have given their Go-Statement EOS will be enabled for public usage.
After that you can transfer/bus tokens from individuals or exchanges.