My primary instrument is Tuba. Among tuba players there are quite a few who build what are called Franken-Tuba's. Basically we find old junk, sometimes buy new components, and build homemade conglomerations.
Is this a thing in the saxophone community?
"FrankenSax" is a term which is used in sax world, yes.
It usually refers to a model that had missing parts or pieces so damaged that they just needed to be replaced. But on a significant scale.
For example....a replacement neck, or modified single KEY, or a new bellbrace or keyguard...makes NOT a Frankensax.
But a horn where someone took the body tube and bow of one model, slapped on a new bellpiece, modified the pinky table mounting and keys to fit that bellpiece....that's a Frankensax.
Or where they replaced the entire vintage pinky assembly with a modern style one, yeah that's Frankensax....
There is a guy here in US, George Borodi,who is actually really GOOD at doing that. Having 2/3 of a horn and piecing together the rest. He also relacquers them so they look brand new. Technically, impressive.
The problem is...he knows that selling them as a Frankensax gets no ca-ching, so he never describes them as such. If you ask him, he tends to be very vague in his answers....which is too bad because honestly, it looks like he does a very thorough job in producing a nicely playing result.