That's the paradox. In DIC most of the fibrin is used up in the body and there will be a negative feedback on clot formation, which leads to bleeding. To prevent it we give vit k.
In DIC there is excess clot formation on one end and haemorrhage as well due to used up clotting factors. The Vit K is used to decrease loss of blood through haemorrhage by coagulation.
Disseminated intravascular coagulation (DIC) is characterized by systemic activation of blood coagulation, which results in generation and deposition of fibrin, leading to microvascular thrombi in various organs and contributing to multiple organ dysfunction syndrome (MODS).
Derangement of the fibrinolytic system further contributes to intravascular clot formation, but in some cases, accelerated fibrinolysis may cause severe bleeding. Hence, a patient with DIC can present with a simultaneously occurring thrombotic and bleeding problem, which obviously complicates the proper treatment.