I have been machine polishing bits and pieces for many years and never had something grabbed. I use loose cloth, not padded cloth, wheels (softer and less likely to grab). The user must never allow the wheel to turn into the object being. Knowing how to used a polishing wheel safely (gloves, eye protection) is very important. Also, when machine polishing alloy, wear a mask or filter to prevent the suspended aluminum oxide from being inhaled (you can actually smell the product soon after the polishing begins...
Machine polishing compounds are available in at least three grades, from coarse to very fine...
Small bits and pieces, that are threaded, can be held by attaching to the end of an appropriate bole.