We know that if we use a PFR it will follow the reaction vector. So if a reaction vector points out of the region we can use a PFR to obtain points outside of the region, thus extending the region. Thus we do not have the entire set of possible products.
Note that a vector that is tangent to the boundary of the region does not point out of the region. If we follow a reaction vector that is tangent to the boundary we will remain on the boundary until the vector is no longer tangent to the boundary. It willl then either point out or into the region at this point.