I am going to assume that by convergent zone, you mean a convergent plate boundary. This being the case, then convergent plate boundary is a general term to describe places where two tectonic plates are converging. That is, they are coming together or colliding. What happens when the plates collides depends on what type of crust is on top of the plate. There are two type of crust, oceanic and continental. Oceanic crust is relatively dense. Continental crust is relatively light. These two types of crust result in three types of convergent zones. The first type is where two plates carrying oceanic crust converge on each other. The second type is where you get a plate with oceanic crust converging on a plate with continental crust. the third type is where you get two plates with continental crust converging. In the case of the first two types of convergent zones, a subduction zone will form as one plate is forced under the other. In the case of the oceanic to oceanic convergence, it will be which ever plate is the coolest. In the case of the oceanic to continental convergence, it will always be the oceanic plate that gets thrust under the continental plate because continental crust is too light to be forced down into the mantle. As plates move, an oceanic basin may close up ultimately leading to the convergence of two continental land masses. Since continental crust cannot be subducted, subduction ceases with the collision between the continents. The oceanic plate that would have been attached to one of the continents and subducted under the other will eventually become detached and continue to sink into the mantle, but that is the end of subduction at that boundary. So, in summery. There are three types of convergent plate boundaries. Two of the types have active subduction zones associated with them. The other type does not. For more information on this and to see some diagrams go to http://wrgis.wr.usgs.gov/parks/pltec/converge.html