We study the electron emission produced by swift protons impinging grazingly on a Be(0001) surface. The process is described within a collisional formalism using the band-structure-based (BSB) approximation to represent the electron-surface interaction. The BSB model provides an accurate description of the electronic band structure of the solid and the surface-induced potential. Within this approach we derive both bulk andsurface electronic states, with these latter characterized by a strong localization at the crystal surface. We found that such surface electronic states play an important role in double-differential energy- and angle-resolved electron emission probabilities, producing noticeable structures in the electron emission spectra....