Yes, indeed, such a thing does exist! I decided to try it out following a helpful post by Rosina Plane in the Mosaic Crochet World FB group - she was kindly given permission from Lisa Richardson, who claims the lock stitch technique as her invention, to share a tutorial with the group. Not only does it produce a reversible look, but it also prevents those dreaded gaps that can occur with the double crochets into the front loop two rows down (and those gaps can become quite unsightly on the back side if the pattern calls for more than a few dc's in succession.
I had seen a YT tut by Susan Lowman (The Crochet Architect) who uses a different technique to prevent gaps (she calls it an anchored dc), but it does not reverse the image on the back. I have seen some people comment that they do not like the added bulkiness caused by this anchored stitch.
Back to Lisa's reversible technique which she explains in a paid design on Ravelry. Her example uses red and white and really shows up the reverse design well. So, I took a graph that I found on Pinterest and gave it a go. I like the result, but have realised that the reverse image is not that visible if your yarn colours do not have a stark contrast. I had thought that my test swatch using a lime green and a cream/beige would show up the reverse far better than it did, but, hey, it's all about learning.
This is the front side of my test square to which I added Tinna's double border just for fun and to refresh my memory on how to do a double border. Unfortunately I realised too late into the pattern that I should have added an extra stitch before the edge stitch so that the left side of the design with the 3 cream/beige dc's does not get lost in the edge.
Here is the reverse image.
