This study is devoted to a submanifold M of codimension 2 of an almost paracontact metric manifold M, for which the Reeb vector field of the ambient manifold is normal. Some sufficient conditions for the existence of M are given. When M is paracosymplectic, then some necessary and sufficient conditions are established for M to fall in one of the following classes of almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: normal, paracontact metric, para- Sasakian, K-paracontact, quasi-para-Sasakian, respectively. When in addition, M is para-Sasakian and M is paracosymplectic, some characterization results are obtained for M to be totally umbilical, as well as a nonexistence result for M to be totally geodesic is provided. The case when M is of a constant sectional curvature is analysed and an example is constructed.