The rule book entry for Harrowed Dudes states:
You may move your Harrowed Dude home booted to cover one casualty.
Therefore, a Harrowed Dude who can't move for whatever reason, can only be assigned 1 casualty if the shootout is in his controller's home.
At which point he'd boot and leave the shootout, but not actually have to move.
This is supported by the previous ruling that a dude under the effects of Jade Stance cannot refuse a callout or flee a shootout outside of their home.
(But can in their home.)
So if you have other dudes in the shootout they'd have to soak the casualties instead, similar to how the original Mario Crane's trait can sometimes be detrimental.