This work is aimed at extending recent studies dealing with the highly excited vibrational dynamics of HOCl [J. Chem. Phys. 111, 6807 (1999); J. Chem. Phys. 112, 77 (2000)], by taking advantage of the fact that the OH-stretch remains largely decoupled from the two other degrees of freedom up to and above the dissociation threshold. The molecule is thus reduced to a two-dimensional (2D) system by freezing the OH bond length to its equilibrium value. All of the calculated bound states of the 2D system, as well as the first 40 resonances, can be assigned with a Fermi polyad quantum number. The bifurcation diagram of the principal families of periodic orbits (POs) is extended to higher energies compared to 3D studies. In particular, the birth of ''inversion'' states (states exploring two equivalent wells connected through the linear HOCl configuration) is related to a period-doubling bifurcation of the families of bending POs, while ''dissociation'' states (states for which the energy flows back and forth along the dissociation pathway) are shown to lie on top of three successive families of POs born at saddle-node bifurcations. Based on the derivation of a classical analogue of the quantum Fermi polyad number, the energies of particular quantum states and classical POs are plotted on the same diagram for the 2D ab initio surface and are shown to agree perfectly. In contrast, comparison of classical Poincaré surfaces of section and quantum Husimi distributions suggests that the classical dynamics of 2D HOCl is much more chaotic than the quantum dynamics. This observation is discussed in terms of the quantum/classical correspondence, and particularly of the vague tori introduced by Reinhardt. It is nevertheless shown that quantum and classical mechanics agree in predicting a slow intramolecular vibrational energy redistribution (IVR) between the OCl stretch and the bend degrees of freedom.