Replicating Lgr5+ stem cells and quiescent Bmi1+ cells behave as intestinal stem cells (ISCs) in vivo. Disrupting Lgr5+ ISCs triggers epithelial renewal from Bmi1+ cells, from secretory or absorptive progenitors, and from Paneth cell precursors, revealing a high degree of plasticity within intestinal crypts. Here, we show that GFP+ cells from Bmi1GFP mice are preterminal enteroendocrine cells and we identify CD69+CD274+ cells as related goblet cell precursors. Upon loss of native Lgr5+ ISCs, both populations revert toward an Lgr5+ cell identity. While active histone marks are distributed similarly between Lgr5+ ISCs and progenitors of both major lineages, thousands of cis elements that control expression of lineage-restricted genes are selectively open in secretory cells. This accessibility signature dynamically converts to that of Lgr5+ ISCs during crypt regeneration. Beyond establishing the nature of Bmi1GFP+ cells, these findings reveal how chromatin status underlies intestinal cell diversity and dedifferentiation to restore ISC function and intestinal homeostasis.