Bitcoins allows the modification and re-issuance of an unconfirmed transaction. The new transaction replaces the previous one. In doing so, all the costs associated with the previous transactions are erased. This could open the door to Denial of Service attacks where multiple transactions were forced on the network each one replacing the previous one.
To avoid this, Bitcoin developers have created the Replace-by-Fee mechanism. It is the replacement of one version of an unconfirmed transaction with another version that pays a higher fee. It is used by Bitcoin miners to sort out multiple versions of the same transaction. Also called RBF.