Designing Kitchens and Bathrooms - exhaust bathroom fan

My bathroom fan died.
I took out the fan, its a miami-carey.
The fan motor was just one piece in the metal box there.
But there is no duct or outlet pipe.
Why would they do this as the fan seems useless unless it is vented outside.

should i even replace the fan/motor.
I don't even know if i can find a replacement fan. Maybe I should just try to find a new motor as that is probably what the problem is.

This is crazy.

I would tend to agree. If the fan does not get the moist air outside, it is causing more problems than it solves. If you can't easily get it to exhaust outside, I certainly would not go looking for a replacement. But big box stores sometimes have replacement motors, or do a search on the web for the manufacturer.

I may be taking your post too literally, but it does not necessarily need to vent outside. Mine cycles air into the attic space which as you know ends up outside. But yes, if the fan is contained within a sealed box then your now broken fan never really served any purpose in the first place. If theres attic space above, by a new unit or i suppose you could just drill a hole in that box. If theres another floor above, well, adding a chase that vents outside can get difficult or pricey, whichever road you take.