  The very high energy (VHE) gamma-ray emission reported from a number of
pulsar wind nebulae (PWNe) is naturally explained by the inverse Compton
scattering of multi-TeV electrons. However, the physical dimensions of some
gamma-ray-emitting PWNe significantly exceed the scales anticipated by the
standard hydrodynamical paradigm of PWN formation. The most "disturbing" case
in this regard is HESS J1825-137, which extends to distances
$r\approx70\rm\,pc$ from the central pulsar PSR J1826-1334. If the gamma-ray
emission is indeed produced inside the PWN, but not by electrons that escaped
the nebula and diffuse in the interstellar medium (ISM), the formation of such
an anomalously extended plerion could be realized, in a diluted environment
with the hydrogen number density $n_{ism}\le10^{-2}\rm\,cm^{-3}$. In this
paper, we explore an alternative scenario assuming that the pulsar responsible
for the formation of the nebula initially had a very short rotation period. In
this case, the sizes of both the PWN and the surrounding supernova remnant
depend on the initial pulsar period, the braking index, and the ISM density. To
check the feasibility of this scenario, we study the parameter space that would
reproduce the size of HESS J1825-137. We show that this demand can be achieved
if the braking index is small, $n\leq2$ and the pulsar birth period is short,
$P_{\rm b}\simeq1\rm\,ms$. This scenario can reproduce the wind termination
position, which is expected at $R_{ts}\simeq0.03\rm\,pc$, only in a dense
environment with $n_{ism}\geq\rm1\,cm^{-3}$. The requirement of the dense
surrounding gas is supported by the presence of molecular clouds found in the
source vicinity.
