From the beginning Katie Thompson knows escaped convict Carl Malcom is going to kill her. He made that clear from the beginnng. Breaking into her apartment and taking her hostage he plays with her emotions while threatening to kill everyone they come in contact with if she leaves him. Forced to follow him to the final showdown where Carl plans on dying, Katie knows he wants her to die with him believing that she'll go to heaven and take him with her.
U.S. Marshall Marcus Warren knows this manhunt is the one that counts more than any of the others. There's no doubt Carl will kill Katie if he's not stopped, so he begins the chase always a step behind. Carl's plan has always been for Marcus to kill him, he just doesn't want it to end the way Carl has in mind, with Katie going first.