The present work presents a critical assessment of claims in recent literature that moribund language varieties exhibit accelerated language decay, and that attrition in individual grammars has a causational relationship with language shift to the majority language. We show these claims to be unfounded. Based on two empirical points taken from moribund heritage varieties of German--complementizer agreement and the restructuring of the morphosyntactic properties of dative case--we provide evidence that (a) attrition in the form of simplification of the heritage grammar is often times minimal, especially when compared to the nonstandard input varieties (rather than to Standard German), and (b) that systematic restructuring of the grammar is a typological pattern in language contact settings. These empirical findings point toward the limited effects of attrition on particular domains of grammar systems across the lifespan.