  We study runaway, kination-dominated epochs in string cosmology. We show how
the apparent classical decompactification runaway of the volume modulus,
described by a kination epoch in the 4-dimensional EFT, can be uplifted to a
classical Kasner solution in 10d in which the non-compact dimensions collapse
towards a Big Crunch. This can also be generalised for arbitrary spacetime and
compactification dimensions. We conclude with some comments on how this picture
is modified by quantum effects, and the need for both dynamical and kinematical
Swampland constraints.
