The terms whiskering, and more generally grafting, refer to adding generators to any monomial ideal to make the resulting ideal Cohen–Macaulay. We investigate the independence complexes of simplicial complexes that are constructed through a whiskering or grafting process, and we show that these independence complexes are (generalized) Bier balls. More specifically, the independence complexes are either homeomorphic to a ball or sphere. In a related direction, we classify when the independence complexes of very well-covered graphs are homeomorphic to balls or spheres.