I made a scrap rug in a workshop once using a plastic handle tool. It was easy. You can make it as big as you like. It takes a lot of fabric for a small rug, I think about 12 yards. I tore up old clothes, tablecloths, sheets, etc. I still have the rug after all these years. I don't have non slip backing but you can buy the non slip pads. I have crocheted fabric strips for small rugs.
Here is a video of one way using the plastic tool.
https://www.youtube.com/watch?v=xV6kRGQnjW4