Given the context of your comment on <PERSON>'s answer above, it looks like you're asking if the continuity equation, $\rho_1A_1v_1 = \rho_2A_2v_2$, applies to blood flow through a local vessel. The answer is that it doesn't, because the local vessel is not a closed system.
The continuity equation is derived from the principle of conservation of mass (see the earlier link) and requires that everything coming in at position 1 exit at position 2. Here, a blood clot, or specifically in your example, a pulmonary embolism, increases the resistance in one of a number of vessels in parallel. Blood flow is diverted to the parallel vessels with lower resistance, the ones without the clot. This is useful in a helpful clot at the site of injury as well as an unhelpful clot like a pulmonary embolism. Thankfully, a clot in an injured vessel has the ability to slow and finally stop the loss of blood. 171
Again, this is allowed despite the continuity equation because there is an alternative path. Blood can either flow out of the vessel at the site of damage, or flow through the vessel.
The fact that changes in vascular resistance are met with changes in flow is a principle used to beneficial effect in normal physiology, not just the response to a clot. Arterioles, for example, regulate flow through vascular beds as needed, by increasing or decreasing resistance.
There is a case, a saddle embolus, where there is no parallel path. Here, though, flow still decreases because the pump fails (and pressure is lost). The rapid increase in resistance cannot be compensated for by the heart, and sudden death results.
Generally, when applying fluid dynamic principles to blood flow and the circulatory system, you have to consider whether the assumptions hold. Generally, you can apply the continuity equation to portions of the circulatory system in series (e.g., the cardiac output of the right heart has to equal the cardiac output of the left heart), but there are still caveats (vessel walls are not rigid -- they have a capacitance).
These principles are discussed in Costanzo Physiology Ch. 4. 171