Often, an additional lens, called a field lens is placed in the telescope focal plane. This does not affect the focal reduction but is used to reimage the telescope pupil somewhere in the focal reducer. One reason this may be done is to minimize the size that the collimator lens needs to be to get off-axis images. The size of the field lens itself depends on the desired size of the field that one wishes to reimage.
Another use of reimaging the pupil is when one is building a coronagraph, an imaging system designed to observe faint sources nearby to very bright ones. The problem in seeing the faint source is light from the bright one, both from scattered light and from diffraction. The solution is to put an occulting spot in the telescope focal plane which removes most of the light from the bright object. However, the diffraction structure is still a problem. It turns out you can remove this by reimaging the pupil after the occulting spot and putting a mask in around the edges which are the source of the diffraction (Lyot stop). The resulting image in the focal plane of the focal reducer is free of both bright source and diffraction structure. To do really well with a coronagraph, one also needs to minimize scattering on the optical surfaces, which requires very smooth lenses which are very clean.
Also, pupil reimagers are widely used in IR systems to reduce emission via cold pupil stops. The issue here is that the telescope itself contributes infrared emission which acts as additional background in your observations. There is little you can do about emission from the primary, since you need to see light from the primary to see your object! However, you can block out emission from regions of the pupils which are obscured already, for example, by the secondary and/or secondary support structures. To do this you put a mask in the pupil plane. Obviously, however, the mask needs to be colder than the telescope itself or else the mask would contribute the background.