In 1845 Adolphe Sax patented the saxotromba as an instrument and as a form to be applied, with modifications, to saxhorns, cornets, trumpets, and trombones. There are no known extant copies of the saxotromba, and a detailed study of its development sheds light on the fate of this family of instruments.
Inconsistent terminology in instrument catalogues, tutors, and other sources of the era complicates the study; but a comparison of measurements taken from Sax’s patent drawings, surviving instruments, and minutes from court proceedings of lawsuits involving the saxotromba shows that dimensions of existing instruments heretofore identified as alto and baritone saxhorns more closely resemble the dimensions of the alto and baritone saxotromba.
This suggests that at some point alto and baritone saxotrombas replaced alto and baritone saxhorns in the saxhorn family. If this is the case, then surviving instruments hitherto considered to be alto and baritone saxhorns are in reality alto and baritone saxotrombas, though the existence of a complete family of saxotrombas indeed appears to have been a fiction.
This according to “The saxotromba: Fact or fiction?” by Eugenia Mitroulia (Journal of the American Musical Instrument Society XXXV  pp. 123–149.
Today is Adolphe Sax’s 200th birthday! Above, his drawings of the soprano and bass saxotrombas (not to scale); below, a somewhat antic trailer for a film about Sax’s life.