In both Canon and Legends, a pair of lightsabers functionally similar to Rey's potential new one were seen in the hands of the Besalisk Jedi Master Pong Krell during the Clone Wars. This picture shows them in their folded and extended configurations:
The lightsabers used by the Jedi Temple Guards in both Canon and Legends were aesthetically and functionally similar to Rey's potential lightsaber, but were only shown to be folding lightsabers in Star Wars Rebels, part of Canon. However, it should be pointed out that in Rebels the folding hilt was seen only in the hands of one Temple Guard, and since lightsabers were personalized weapons, it is possible that not every Temple Guard weapon had that feature.
Lightsabers in the hands of the Temple Guard during the Clone Wars:
Clone Wars Concept Art (note slanted emitter shrouds and lack of hinged section, unlike Pong Krell's lightsaber):
And while another answer already uses this video, I will include it for the sake of completeness and to point out the lightsaber at 1:32 that appears to be the same as the Clone Wars Temple Guard weapon: