as for folding, or twisting, this is a problem we all battle. as said above, try a slightly tighter weave. that adds a stifness that can help also incorporating a second weave, at intervals can be a design feature that looks good, and can help with the twisting. adding a persian (HP-3-1 or 4-1 works best) strip an inch and a half or so at even intervals gives it the lateral stability that a round weave can lack.
This is also a good option if you already have a tennis necklace that is flipping. Abitbol adds that shorter tennis necklaces are less likely to flip because there is more tension on the chain. You can go to a jeweler to have your necklace shortened, or look for a shorter design when shopping for a new one.
too heavy a clasp for your necklace. it will always work towards the front. the clasp needs to be lighter than the pendant weight. and yes, if you attach to the chain and wire it, it will twist with the chain. you need to attach alone with a jumpring so it dangles instead. un-attach it, and dangle instead. problem solved.
The layered necklace detangler is a necklace clasp that can hold onto 2-4 necklaces at a time. It helps keep your necklaces from getting tangled as you go on about your day. It also keeps your necklace clasps all together in one spot so that you don’t have to adjust the necklaces one at a time!
Wear a nice size pendant to keep it in place. A diamond cross or other design so that there is additional weight in the front which will keep the necklace from flippin. luvednotspoiled
Method of stabilizing a necklace. United States Patent 6138356. Abstract: A stabilizer accessory for necklaces to keep the necklace from twisting about the wearer's neck. The stabilizer is an elongate approximately oval-shaped metal loop which is connected as by clasps to the necklace ends, and rests on the nape of the neck of the wearer. The presence of the stabilizer causes the necklace to resist twisting of the necklace, stabilizing the necklace in its proper position.