Santa used to get his cap tied to a tree branch every year, but I would rather not do that, and both have tie outs from the midsection. I can't understand how tying fishing line over the top would help.
If these are the blow-ups with the fans/blowers, you can put a couple of "ziploc " baggies full of sand inside. Just open the zipper that lets the air out and space them around the bottom. Then zip it up and re-inflate.