The prolyl-specific peptidase fibroblast activation protein-α (FAP-α) is expressed at very low or undetectable levels in nondiseased human tissues but is selectively induced in activated (myo)fibroblasts at sites of tissue remodeling in fibrogenic processes. In normal regenerative processes involving transient fibrosis FAP-α ⁺ (myo)fibroblasts disappear from injured tissues, replaced by cells with a normal FAP-α ^- phenotype. In chronic uncontrolled pathological fibrosis FAP-α ⁺ (myo)fibroblasts permanently replace normal tissues. The mechanisms of regulation and elimination of FAP-α expression in(myo)fibroblasts are unknown. According to a yeast two-hybrid screen and protein databanks search, we propose that the intracellular (co)-chaperone BAG6/BAT3 can interact with FAP-α, mediated by the BAG6/BAT3 Pro-rich domain, inducing proteosomal degradation of FAP-α protein under tissue homeostasis. In this Perspective, we discuss our findings in the context of current knowledge on the regulation of FAP-α expression and comment potential therapeutic strategies for uncontrolled fibrosis, including small molecule degraders (PROTACs)-modified FAP-α targeted inhibitors.