  A group has Property $\mathrm{(NL)}$ if it does not admit a loxodromic
element in any hyperbolic action. In other words, a group with this property is
inaccessible for study from the perspective of hyperbolic actions. This
property was introduced by Balasubramanya, Fournier-Facio and Genevois, who
initiated the study of this property. We expand on this research by studying
Property $\mathrm{(NL)}$ in Coxeter groups, a class of groups that are defined
by an underlying graph. One of our main results show that a right-angled
Coxeter group (RACG) has Property $\mathrm{(NL)}$ if and only if its defining
graph is complete. We then move beyond the right-angled case to show that if a
defining graph is disconnected, its corresponding Coxeter group does not have
Property $\mathrm{(NL)}$. Lastly, we classify which triangle groups (Coxeter
groups with three generators) have Property $\mathrm{(NL)}$.
