This paper presents a novel scheme for estimating states and faults for a class of infinitely unobservable descriptor systems using sliding mode observers (SMOs). Treating certain states of the original infinitely unobservable system as unknown inputs results in a reduced-order system that is infinitely observable. Then by designing the SMO based on the reduced-order system, state estimation and fault reconstruction is achieved, thus relaxing the infinite observability requirement of the original system. The necessary and sufficient conditions in terms of the original system matrices are also investigated. A simulation example verifies the claims made in this paper.