The signed count is invariant under framed cobordism

(Orientations of $W$ and of its normal bundle.) Orient the normal bundle $\nu (W\subseteq M\times I)$ by the framing $\mathrm{\Psi }$, and orient the $1$-manifold $W$ by the rule that a positive normal frame followed by a positive tangent frame of $W$ is a positive frame of $T(M\times I)$; this orientation exists and is unique because $W$ is connected componentwise and the rank of $\nu (W)$ is $m$. With this choice the orientation of $W$ is determined by the framing and the product orientation, and no orientation is imposed on the individual points of the $N_i$.

On an end collar a normal frame given by ${\mathrm{\Psi }}^{-1}$ is a frame $b$ of $T_{x}M$ of sign $\epsilon (x)$. In the product orientation, $(b,\epsilon (x){\mathrm{\partial }}_t)$ is positive, so the rule in step 1.1 makes $\epsilon (x){\mathrm{\partial }}_t$ the positive tangent of $W$ there. At the bottom, the outward tangent is $-{\mathrm{\partial }}_t$, so the boundary point sign is $-\epsilon (x)$; at the top it is $+\epsilon (x)$. Consequently the signed boundary count is $-{\mathrm{\Sigma }}_0+{\mathrm{\Sigma }}_1$. This computes the signs directly on $W$, without suppressing the dimension-dependent signs of the ambient faces.

By [F2] the signed count of the boundary of a compact oriented $1$-manifold is zero, so $-{\mathrm{\Sigma }}_0+{\mathrm{\Sigma }}_1=0$ and ${\mathrm{\Sigma }}_0={\mathrm{\Sigma }}_1$: the signed count is a framed cobordism invariant. Consequently a closed framed $0$-manifold consisting of exactly two points of the same framing sign and no other points has signed count $\pm 2\mathrm{\ne }0$, while the empty framed $0$-manifold has signed count $0$, so it is not framed null-cobordant; a pair of opposite signs in a common chart ball is framed null-cobordant by [F3].