Normally speaking it does not happen because of the presence of an anti-coagulant present in blood -heparin. But we do have some rare cases of clotting inside intact blood vessels. There are two types of such clot. First one , thrombus clot are static clots which grow bigger with time and ultimately block the vessel. The other one is ambolus clot, they are the moving clots and may ultimately get dissolved in blood . But the latter ones are more dangerous due to their moving nature
Blood clots may form inside small veins near the surface of your skin (superficial phlebitis), resulting in localized redness, pain and swelling. Superficial phlebitis rarely causes complications and requires minimal treatment. Blood clots that form inside larger, deeper veins (deep vein thrombosis) may cause more-widespread symptoms in the affected area, usually your leg, and can cause more-serious problems.