I tied a piece of ribbon on the handle of my scissors. The rest of the family can use any scissors in the house that doesn't have a piece of ribbon on the handle. Before that I always heard "I didn't know those were your good scissors..." Not only does it identify my scissors but it also helps me find them if they are under a pile of fabric or stuff. I have a short piece of ribbon on my dressmaker scissors but on my small scissors that I use by my machine and for hand sewing I have a long piece of ribbon on the handle so I can wear my scissors around my neck when I'm sitting on the couch so I don't lose them in the cushions and when I'm at the machine I loop the ribbon around a spindle on the machine so if they get pushed off the table they won't fall all the way to the floor but can still use them by the machine without unlooping the ribbon. I had a good pair ruined one day when it fell point down on a tile floor and bent the point.
Looking at the picture of the curved scissors that have fallen on the floor, I don't have an answer. Mine don't lay like that but they are also not left handed so don't know if that's something unique to left handed scissors or perhaps that brand.