Does it have a pneumatic tire?
Replica high-wheel bicycles are currently available, and go for $1200 or so new. I may be mistaken, but I think all of them had a fixed hub, not a coaster hub. Both the originals and all of the replicas have solid rubber tires.
Coker introduced a smaller high-wheel bicycle called the Wheelman, with a 36" pneumatic tire. And they DID have a coaster-type hub. Those tires are more commonly used on Coker (and other brand) unicycles now. There was also a Monster Cruiser that used the 36" tires. I think the Wheelman sold for $400 or $500 new, it was cheaper than the regular high-wheel replicas.
(The terminology is confusing, but "boneshaker" was normally applied to an even older style of bicycle, not the high-wheel bikes. I think the early "safety bicycles" also used the solid tires, so that was not specific to the high-wheel bikes. However, "Boneshaker" is one of the model names for current reproductions.)
If the bike in question IS the Wheelman, and the hub is toast, and cannot be practically repaired, check into whether the hub can be replaced with a unicycle hub. This might require welding modifications to the forks. This would result in a fixed-gear cycle, but at least rideable.