Thanks for your reply, Flash saves data on the computer storage, in temporary folders like App_Data, it's called SharedObject in flash. Yeah the url needs surely to match, otherwise the brower sees it as a new element to download, and create a new folder for it.
I think the detection of stealing must be on the developer side if he wants to avoid this, it can be done IN the game. Or maybe an option for flash game on itch.io, "persistant URL".
It's weird nobody notice it before, a lot of flash games needs to save datas like this.