Subpopulations of soluble, misfolded proteins can bypass chaperones within cells. The extent of this phenomenon and how it happens at the molecular level are unknown. Through a meta-analysis of the experimental literature we find that in all quantitative protein refolding studies there is always a subpopulation of soluble but misfolded protein that does not fold in the presence of one or more chaperones, and can take days or longer to do so. Thus, some misfolded subpopulations commonly bypass chaperones. Using multi-scale simulation models we observe that the misfolded structures that bypass various chaperones can do so because their structures are highly native like, leading to a situation where chaperones do not distinguish between the folded and near-native-misfolded states. More broadly, these results provide a mechanism by which long-time scale changes in protein structure and function can persist in cells because some misfolded states can bypass components of the proteostasis machinery.