– 2 – the stars monitored by Kepler (Rowe et al. 2010, hereafter R2010). Each of two “Kepler Objects of Interest” (KOIs) has exhibited repeating transits, and intervening eclipses that are deeper than the transits. In KOI-81, it is estimated that the luminosity and temperature of the compact companion, KOI-81b, are 0 . 4 L ⊙ and ∼ 13 , 000K, respectively. For KOI-74b the estimates are L = 0 . 03 L ⊙ and T ∼ 12 , 000K. These small objects have temperatures ten times higher than would be consistent with heating by the star alone. We explore the possibility that the hot compact objects are the cores of stars whose evolutions were interrupted by binary interactions, focusing on the implications for the Kepler mission and for fundamental science. In § 2 we consider the general evolutionary sequences that may have produced KOI-81 and KOI-74. We turn in § 3 to the question of the likelihood of detecting the products of mass transfer in the Kepler data set. We show that many more systems that have experienced mass transfer are likely to be discovered by Kepler , making the mission a unique tool for the study of interacting binaries. Because the eclipse depths and orbital separations of some white-dwarf/blue-straggler binaries are similar to what is expected of terrestrial planets orbiting in the habitable zones of their host stars, it is important to distinguish between the two possibilities. Mass measurements are crucial. An interesting consequence of the higher mass of white dwarfs relative to planets is that white dwarfs can produce detectable lensing of the stars they orbit. The magnification associated with lensing can balance the dimming associated with a normal transit, or it can produce a net magnification (Sahu & Gilliland 2003; Farmer & Agol 2003; Agol 2003). We incorporate the effects of lensing in § 4 and summarize our results in § 5. When a white dwarf orbits a main-sequence star, the progenitor of the white dwarf must have initially been the most massive star in the binary. Let M 1 (0) denote the initial mass of the primary. If the mass of the white dwarf, M$_{c}$, is smaller than that of the remnant normally produced by a star of this mass, we can infer that the evolution of its progenitor was truncated through interaction with the secondary. The interaction may have been stable, producing a gradual erosion of the primary through mass transfer. Or it may have been unstable, producing an almost explosive disruption of the primary. In either case, the mass M of the main-sequence star we observe today may be larger than its initial mass, M 2 (0) . Such a star is called a blue straggler, in analogy to stars in clusters that appear to be more massive than the cluster turn-off. 2. Erosion and Disruption 2.1. Evolutionary sequences