  We study the Aw-Rascle system in a one-dimensional domain with periodic
boundary conditions, where the offset function is replaced by the gradient of
the function $\rho_{n}^{\gamma}$, where $\gamma \to \infty$. The resulting
system resembles the 1D pressureless compressible Navier-Stokes system with a
vanishing viscosity coefficient in the momentum equation and can be used to
model traffic and suspension flows. We first prove the existence of a unique
global-in-time classical solution for $n$ fixed. Unlike the previous result for
this system, we obtain global existence without needing to add any
approximation terms to the system. This is by virtue of a $n-$uniform lower
bound on the density which is attained by carrying out a maximum-principle
argument on a suitable potential, $W_{n} = \rho_{n}^{-1}\partial_{x}w_{n}$.
Then, we prove the convergence to a weak solution of a hybrid free-congested
system as $n \to \infty$, which is known as the hard-congestion model.
