Mudrex is an open book exchange i.e. when a user places an order to buy/sell a particular asset at the quoted price, Mudrex tries to find the corresponding sell/buy order for the same.

Let's consider an example where a User A has placed an order to buy 100 Ripple at a price of 50 each. On the sell side, the is a user B who is willing to sell 20 Ripple at 50 each. In this case, the Mudrex matching engine will match the orders placed by Users A and B. User B's order will be completely filled  while the order placed by User A will be partially filled.

Post this, the order placed by User A will continue to exist except that the quantity required to be filled now is just 80 Ripple tokens. The above i known as partial execution. 

User A can still go ahead and cancel the order however any tokens partially executed cannot be returned.