Bathroom Fan - No Vent?

We are attempting to replace a bathroom fan in a first floor bathroom (full bath) in a two story home. After removing the original fan motor and inspecting the fan housing we found there is no duct system connected and that the fan is venting directly into the space between the floors. While this is the least used bath of the home, I am very concerned about venting moisture directly between the floors! The fan may have originally vented to the side of the home, but previous owners constructed an addition that would have blocked the logical original venting area and do not appear to have compensated. To complicate matters, we are sure the fan was installed with the original construction and is attached directly to the ceiling beam with no easy access to remove without significant damage to the ceiling. There appears to be no logical path to vent to the exterior of the home without encountering major structural elements.

Any ideas out there on how to figure out a venting path? Does anyone know of any replacement fans that might have a recirculation feature for hard to vent areas that might work as well?

Venting into the attic space says check for mold!

While a pain, you can usually tear an old fan out by prying and cutting and smashing. Just make sure the power is off first.

There may not be a good path to run a vent. From your description, it appears the bathroom does not have an exterior wall. The choices are to see if you have a clear path to the outside the way the joist bay runs, or to see if there's a way to route it up, maybe through the closet or some other path, up into the attic where you could either go out the roof or out a sidewall.

Once you've banged, smashed, crushed the old one to get it out, you can stick your head up there and maybe see if you have a path to the exterior.

Other than that, maybe a tabletop air cleaner with a carbon filter might help. If this is a full bath, code requires either an operable window or a true vent.