  The majority of massive stars are formed in multiple systems and will
interact with companions via mass transfer. This interaction typically leads to
the primary shedding its envelope and the formation of a "stripped star".
Classically, stripped stars are expected to quickly contract to become hot
UV-bright helium stars. Surprisingly, recent optical surveys have unveiled a
large number of stripped stars that are larger and cooler, appearing
"puffed-up" and overlapping with the Main Sequence (MS). Here, we study the
evolutionary nature and lifetimes of puffed-up stripped (PS) stars using
stellar-evolution code MESA. We computed grids of binary models at four
metallicities from Z = 0.017 to 0.0017. Contrary to previous assumptions, we
find that stripped stars regain thermal equilibrium shortly after the end of
mass transfer. Their further contraction is determined by the rate at which the
residual H-rich envelope is depleted, with the main agents being H-shell
burning (dominant) and mass-loss in winds. The duration of the PS star phase is
1$\%$ of the total lifetime and up to 100 times more than thermal timescale. We
explored several relevant factors: orbital period, mass ratio, winds, and
semiconvection. We carried out a simple population estimation, finding that
$\sim$0.5-0.7 $\%$ of all the stars with $\log (L/L_{\rm \odot}$) $>$ 3.7 are
PS stars. Our results indicate that tens to hundred of PS stars may be hiding
in the MS population, disguised as normal stars: $\sim$100 in the Small
Magellanic Cloud alone. Their true nature may be revealed by low surface
gravities, high N enrichment, and likely slow rotations
