In the context of extra dimensional field theories on orbifolds, we study the Dirac equation of chiral fermions on a regularized version of the two-dimensional orbifold T^2/Z_2. This study shows how localized and bulk fermions arise as the resolved space approaches the orbifold limit. It is also explicitly shown how a resolution of the orbifold puts severe constraints on the allowed chiralities and charges of the massless four dimensional fermions, localized or not, that can be present in the orbifold. The limit in which T^2/Z_2 (and its corresponding resolved space) collapses to S^1/Z_2 is also studied in detail.

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