That's really interesting. I don't know what it is
It looks like a spiderwort AKA wandering Jew fell in love with a jade a made a beautiful baby.
I would not cut it.. I don't know what it is- but this would work for many succulents or wandering jew.
Lay it down in a very shallow trench ( one you could make with the tip of a pencil where the whole stem is touching earth, but not buried) in a substrate that will hold a good amont of water to sustain humidity, like peat. Which is not something I would pot it in if it does root - just for rooting- to send that signal- water this way! and keep it from desiccating while it sends roots in that direction. Start with wet substrate and I would keep it damp enough ONLY that the top feels cool to the touch, but not wet/moist/damp. Just cool. Put it in a place that gets indirect sun.
I have a little peat bin (actually a lasana pan) where I throw fallen leaves on my south patio behind one of my larger planters- so it stays warm but avoids direct sun and its amazing what sprouts in that warm shade. Protect it from direct sunlight, or it will crisp up like burnt toast. Can't wait to see what happens!