A DVT is a clot in one of the large veins in your legs. If it breaks loose, it travels to your right atrium via the inferior vena cava. From there it travels through the tricuspid valve into your right ventricle where it gets pumped into the pulmonary arteries. Once there the size of the clot becomes important. It will get lodged somewhere.
Small clots block small blood vessels and there are plenty of others to allow sufficient blood flow for it to not cause a problem. In fact, most of us routinely catch tiny clots in our lungs where they are broken down rather quickly.
However, a big enough clot will cause enough of a blockage that very little blood gets through to the alveoli. Thus almost no blood gets oxygen and travels to the left side of your heart which is responsible for pumping to your body (in particular your brain). Consequently, with your left ventricle not getting any blood to pump, your blood pressure plummets and you drop like a stone. Death can be near immediate.
OK, so that is a pulmonary embolism, but can DVTs cause strokes? Actually YES!
When you are in your mother's womb, you have a hole between your right atrium and left atrium called the foramen ovale. It is part of the system that allows you to live off oxygen provided by mom through the placenta and umbilical cord. When your are born, this hole typically closes off within a few days. Depending on the study, between 10% and 25% of them never fully close. Thus, a clot can theoretically enter the right atrium go through the patent foramen ovale (AKA "PFO") and then get pumped straight to your brain. Normally there is a pressure gradient between the left side of your heart and right side that prevents flow in this direction but certain circumstances such as coughing can temporarily causes some flow from the right to the left. In this situation, a stroke could occur but it is unlikely. A person with atrial fibrillation which causes accumulation of clots in your atrium is more likely to experience a stroke of this nature, but that is another TLDR post...