Gabor systems $\mathcal{S}(g,\Lambda)=\{ M_\xi T_x g : (x,\xi)\in \Lambda \}$ given by translations and modulations of a function $g$ in $G$, where $\Lambda\subseteq G\times\widehat{G}$ has little or no structure, arise naturally. In this work, we focus on studying the frame properties of such systems in the context of expansible locally compact abelian groups, as well as the differences that arise compared to the Euclidean case.