Protein aggregation is associated with a growing list of human diseases. A substantial fraction of proteins in eukaryotic proteomes constitutes a proteostasis network—a collection of proteins that work together to maintain properly folded proteins. One of the overarching functions of the proteostasis network is the prevention or reversal of protein aggregation. How proteins aggregate in spite of the anti-aggregation activity of the proteostasis machinery is incompletely understood. Exposed hydrophobic patches can trigger degradation by the ubiquitin-proteasome system, a key branch of the proteostasis network. However, in a recent study, we found that model glycine (G)-rich or glutamine/asparagine (Q/N)-rich prion-like domains differ in their susceptibility to detection and degradation by this system. Here, we expand upon this work by examining whether the features controlling the degradation of our model prion-like domains generalize broadly to G-rich and Q/N-rich domains. Experimentally, native yeast G-rich domains in isolation are sensitive to the degradation-promoting effects of hydrophobic residues, whereas native Q/N-rich domains completely resist these effects and tend to aggregate instead. Bioinformatic analyses indicate that native G-rich domains from yeast and humans tend to avoid degradation-promoting features, suggesting that the proteostasis network may act as a form of selection at the molecular level that constrains the sequence space accessible to G-rich domains. However, the sensitivity or resistance of G-rich and Q/N-rich domains, respectively, was not always preserved in their native protein contexts, highlighting that proteins can evolve other sequence features to overcome the intrinsic sensitivity of some LCDs to degradation.