So far as I know, this is possible. In an oscillating universe, each cycle is supposed to end with the complete annihilation of all the information contained in the evolution of matter. No information 'leaks' into the next cycle because, presumably, the information about the smoothness of the gravitational field of the universe and the composition of matter, is reduced to a smooth, homogeneous soup of elementary particles. In some versions of oscillatory cosmology, the bounce is 'weak' and some information manages to leak through into the next cycle. The problem is that information about how matter was clumped is probably the first to be lost because during the 'leaky bounce' the gravitational field of the universe is undergoing tremendous fluctuations near the Planck Scale, and the GUt phase transition is inflating away all previous structure, so that none of this information is likely to survive. Also, the oscillatory universe theory is only valid if it can be shown that there is enough mass in the universe to cause re-collapse, and even then it is not possible to predict what will happen after re-collapse.