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There is a well-known finiteness condition for vertex operator algebras and their modules called C_n-cofiniteness. It was shown by Geoffrey Buhl that C_2-cofiniteness of a CFT-type vertex operator algebra is strong enough to guarantee that all of its finitely-generated weak modules are C_n-cofinite for all n > 0. In this talk, we will discuss the extension of Buhl's result to the twisted case, i.e. the orbifold CFT setting. Given a vertex operator algebra V with a general automorphism g of V, we introduce a notion of C_n-cofiniteness for weak g-twisted V-modules. When V is C_2-cofinite and of CFT type, we show that all finitely-generated weak g-twisted V-modules are C_n-cofinite for all n > 0. This talk is based on my work https://arxiv.org/abs/2510.26657.