Find an example such that $\tau$ is a stopping time and $\mathcal{F}_\tau$ and $\mathcal{F}_\infty$ differ on $\{\tau = \infty\}$.

Question

I need to find an example such that the following is true:

$\tau$ is a stopping time and $\mathcal{F}$ is a filtration defined on $\mathbb{R}_+$. Let $\mathcal{F}_\tau$ denote the stopped $\sigma$-algebra, and $\mathcal{F}_\tau$ and $\mathcal{F}_\infty$ differ on $\{\tau = \infty\}$.