Wrap The Strap

This is my wife's genius extra precaution while grocery shopping because you can't keep your eye on your purse 100% of the time and carrying it is a pain in the you-know-what.  She removes the strap from one side of her purse, wraps it through the cart and reattaches it.  If someone tries a quick snatch-and-grab, they end up dragging the cart with them and creating a scene.  Obviously not a complete safety solution, but stopping stupid thieves doesn't always take one.