Accessible parts of the boundary for domains with lower content regular complements

We show that if $0<t<s\le n-1$, $\mathrm{\Omega }\subseteq {\mathbb{R}}^n$ with lower $s$-content regular complement, and $z\in \mathrm{\Omega }$, there is a chord-arc domain ${\mathrm{\Omega }}_z\subseteq \mathrm{\Omega }$ with center $z$ so that $\mathscr{H}^{t}{\infty}(\partial\Omega{z}\cap \partial\Omega)\gtrsim_{t} $\text{dist}$(z,\Omega^{c})^{t}$. This was originally shown by Koskela, Nandi, and Nicolau with John domains in place of chord-arc domains when $n=2$, $s=1$, and $\mathrm{\Omega }$ is a simply connected planar domain. Domains satisfying the conclusion of this result support $(p,\beta )$-Hardy inequalities for $\beta <p-n+t$ by a result of Koskela and Lehrb"{a}ck; Lehrb"{a}ck also showed that $s$-content regularity of the complement for some $s>n-p+\beta$ was necessary. Thus, the combination of these results gives a characterization of which domains support pointwise $(p,\beta )$-Hardy inequalities for $\beta <p-1$ in terms of lower content regularity.