  We consider a totally asymmetric simple exclusion on $\mathbb{Z}$ with the
step initial condition, under the additional restriction that the first
particle cannot cross a deterministally moving wall. We prove that such a wall
may induce asymptotic fluctuation distributions of particle positions of the
form $$ \mathbb{P}\Big(\sup_{\tau\in \mathbb{R}}\{\textrm{Airy}_2(\tau)
-g(\tau)\}\leq S\Big)$$ with arbitrary barrier functions $g$. This is the same
class of distributions that arises as one-point asymptotic fluctuations of
TASEPs with arbitrary initial conditions. Examples include Tracy-Widom GOE and
GUE distributions, as well as a crossover between them, all arising from
various particles behind a linearly moving wall.
  We also prove that if the right-most particle is second class, and a linearly
moving wall is shock-inducing, then the asymptotic distribution of the position
of the second class particle is a mixture of the uniform distribution on a
segment and the atomic measure at its right end.
