Crystallographic shear (CS) planes provide a new structure-generation mechanism in the anion-deficient perovskites containing lone-pair cations. Pb2Sr2Bi2Fe6O16, a new n = 6 representative of the A(n)B(n)O(3n-2) homologous series of the perovskite-based ferrites with the CS structure, has been synthesized using the solid-state technique. The structure is built of perovskite blocks with a thickness of four FeO6 octahedra spaced by double columns of FeO5 edge-sharing distorted tetragonal pyramids, forming 1/2[110](101)p CS planes (space group Pnma, a = 5.6690(2) Å, b = 3.9108(1) Å, c = 32.643(1) Å). Pb2Sr2Bi2Fe6O16 features a wealth of microstructural phenomena caused by the flexibility of the CS planes due to the variable ratio and length of the constituting fragments with {101}p and {001}p orientation. This leads to the formation of "waves", "hairpins", "Γ-shaped" defects, and inclusions of the hitherto unknown layered anion-deficient perovskites Bi2(Sr,Pb)Fe3O8.5 and Bi3(Sr,Pb)Fe4O11.5. Using a combination of diffraction, imaging, and spectroscopic transmission electron microscopy techniques this complex microstructure was fully characterized, including direct determination of positions, chemical composition, and coordination number of individual atomic species. The complex defect structure makes these perovskites particularly similar to the CS structures in ReO3-type oxides. The flexibility of the CS planes appears to be a specific feature of the Sr-based system, related to the geometric match between the SrO perovskite layers and the {100}p segments of the CS planes.