In the framework of Soft-Collinear Effective Theory, I discuss factorization theorems describing an energetic hadron fragmenting from a jet where the jet invariant mass is measured. The analysis yields a ``fragmenting jet function'' which is related both to the inclusive jet function and to the standard non-perturbative fragmentation function. A simple replacement rule is derived to allow any factorization theorem depending on a jet function to be converted to a semi-inclusive process with a fragmenting hadron.