There is no one answer which could be used to answer your question. Blood clots and artheromatous deposits are the major causes of all deaths.

Blood clots cause death by blocking the blood supply to organs and tissues. When organs and tissues do not receive oxygenated blood and nutrients they die from ischaemia.

Very small clots do not cause death of a person. Large clots cause the death of the tissue or organ supplied. If the organ is essential then the person dies.

Blood clots are treated with the aid of clot busters. These are medications which dissolve clots. Rember these make the blood very thin. So, sometimes a person may die as a result of these medications. Examples are Streptokinase, TPN etc.

At other times doctors may use heparin to prevent the clot from getting larger.

Aspirin prevents clot formation.

Yes, some patients die during treatment but lots of things have to go wrong for death to occur.

Good luck, I hope I have answered your question.
References :
RN

1. Venous thromboembolism (VTE) refers to two serious conditions: deep-vein thrombosis (DVT) and pulmonary embolism (PE).
2. Two million Americans each year develop deep-vein thrombosis (DVT).
3. Deep-vein thrombosis involves the formation of a blood clot in one of the large veins of the upper or lower limbs or pelvis. Blood clots form when circulation to particular parts of the body is abnormally sluggish and/or damage to the blood vessel has occurred. If the blood clot breaks free and travels through the veins, it can reach the lungs, obstructing the pulmonary artery, or its branches, which supply the lungs with blood. If the clot is large and completely blocks a vessel, it can cause sudden death.
4. It is estimated that 600,000 patients with deep-vein thrombosis develop pulmonary embolism each year, with PE responsible for up to 200,000 deaths.
5. According to the American College of Chest Physicians, fatal pulmonary embolism may be the most preventable cause of hospital death.
6. Blood clots in the lungs (pulmonary emboli) kill 200,000 people each year, more than AIDS, breast cancer and highway accidents combined.
7. Risk factors for developing blood clots include pregnancy, obesity, recent surgery, chemotherapy treatment, estrogen use and prolonged immobilization.
8. Risk factors for developing DVT include: acute medical illness; orthopedic, lower extremities, or pelvic surgery; cancer or chemotherapy; chronic heart or respiratory failure; inherited or acquired predisposition to clotting; varicose veins; obesity; pregnancy; birth control pills; postmenopausal hormone replacement therapy; advanced age; prolonged immobilization; and long-distance travel.
9. DVT commonly occurs in one leg. Symptoms may include tenderness, pain, swelling and discoloration or redness. The pain caused by DVT may be a dull ache or cramp in the leg that is severe or mild and is often aggravated by putting weight on the leg. About half the time, though, the problem causes no symptoms.
10. The signs of PE can range from a little shortness of breath to severe cardiopulmonary shock.
11. Anyone who experiences these symptoms (or any unusual symptoms) should immediately seek medical attention. Fortunately, the medications that physicians use to treat DVT may help to resolve the symptoms while preventing serious complications.
12. Traditional treatments for DVT include bed rest, elevation of the affected limb, use of compression stockings and drugs to prevent blood clotting.
13. Anticoagulants, or blood-thinning drugs, work by altering the body’s normal blood-clotting process and may help to prevent PE. The most commonly used anticoagulants are unfractionated heparin, low-molecular-weight heparin, and warfarin sodium.
References :
Sources

Dalen JE, Paraskos JA, Ockene IS, Alpert JF, Hirsh J. Venous thromboembolism: scope of the problem. Chest 1986; 89 (suppl):370S-373S.

Clagett PG, Anderson FA, Heit J, Levine MN, Wheeler HB. Prevention of venous thromboembolism. Fourth ACCP Consensus Conference on Antithrombotic Therapy. Chest 1995; 108 (suppl 4):312S-334S.