When a deep vein thrombosis (DVT) forms, the major risk is that a piece of it breaks off and lodges somewhere in the pulmonary circulation. The pulmonary capillaries are so small that even red blood cells can't make it through with out outrageous contortions, and so for all intents and purposes, dangerous clots can go no further. Any emboli from a DVT will cause pulmonary problems, but they can't, for instance, lodge in the systemic arterial system.
Except that, very rarely, they do. But how? Such "paradoxical emboli" arise when a great coincidence occurs: the patient has a DVT and the patient has some cardiac lesion whereby the right side communicates with the left side. Usually, this is an atrial septal defect. In such a case, it is possible for a DVT's embolus to bypass the lung's capillary filters altogether and skip straight to the left heart. From there, it can go on its merry way and block off a part of the systemic circulation. How rude!