  We propose a new regime of minimal QCD axion dark matter that lies between
the pre- and post-inflationary scenarios, such that the Peccei-Quinn (PQ)
symmetry is restored only on sufficiently large spatial scales. This leads to a
novel cosmological evolution, in which strings and domain walls re-enter the
horizon and annihilate later than in the ordinary post-inflationary regime,
possibly even after the QCD crossover. Such dynamics can occur if the PQ
symmetry is restored by inflationary fluctuations, i.e. the Hubble parameter
during inflation $H_I$ is larger than the PQ breaking scale $f_a$, but it is
not thermally restored afterwards. Solving the Fokker-Planck equation, we
estimate the number of inflationary e-folds required for the PQ symmetry to be,
on average, restored. Moreover, we show that, in the large parts of parameter
space where the radial mode is displaced from the minimum by de Sitter
fluctuations, a string network forms due to the radial mode oscillating over
the top of its potential after inflation. In both cases we identify order one
ranges in $H_I/f_a$ and in the quartic coupling $\lambda$ of the PQ potential
that lead to the late-string dynamics. In this regime the cosmological dark
matter abundance can be reproduced for axion decay constants as low as the
astrophysical constraint $O(10^8)$ GeV, corresponding to axion masses up to
$10^{-2}~{\rm eV}$, and with miniclusters with masses as large as
$O(10)M_\odot$.
