  We analyze the topological properties of a chiral ${p}+i{p}$ superconductor
for a two-dimensional metal/semimetal with four Dirac points. Such a system has
been proposed to realize second-order topological superconductivity and host
corner Majorana modes. We show that with an additional $\mathsf{C}_4$
rotational symmetry, the system is in an intrinsic higher-order topological
superconductor phase, and with a lower and more natural $\mathsf{C}_2$
symmetry, is in a boundary-obstructed topological superconductor phase. The
boundary topological obstruction is protected by a bulk Wannier gap. However,
we show that the well-known nested-Wilson loop is in general unquantized
despite the particle-hole symmetry, and thus fails as a topological invariant.
Instead, we show that the higher-order topology and boundary-obstructed
topology can be characterized using an alternative defect classification
approach, in which the corners of a finite sample is treated as a defect of a
space-filling Hamiltonian. We establish "Dirac+$({p}+i{p})$" as a sufficient
condition for second-order topological superconductivity.
