In Japan, the dead are usually cremated. Unlike other cultures where the remains are ash, a Japanese crematorium uses a different process where the remains are not only ash but also bones.
The relatives then place the bones into an urn. The ritual involves one person lifting a bone using special chopsticks, then passing it to another person with chopsticks, who places the bone into the urn.
The Japanese word for "chopsticks" is hashi which also means "bridge", and in Buddhism there's a bridge over the river boundary between this world and the next. The ritual of passing the bones using chopsticks hopes the deceased will now cross the river successfully.
In a different social occasion, when having a meal with friends you must not pass food to another person using chopsticks because that mimics the same funeral ritual. In doing that, you are sending the recipient to the other world.
Passing food from chopstick to chopstick is taboo in Japan, because not only does it reenact the funeral ritual, but more because it is bad dining etiquette.
Japanese people have strong awareness of personal hygiene. Whether your eating utensils are chopsticks, a knife and fork, or just your fingers which go into your mouth with your food, it's taboo to pass food using your utensils instead of the proper serving utensils.
So while the superstition means the recipient will die, a much more likely result of passing food from chopstick to chopstick is that you will never be invited to dinner again!
You might hear of other "superstitions" about chopsticks, but most tend to be about etiquette rather than invoking something ominous. For example, it's frowned upon to insert chopsticks vertivally in a bowl or rice, since that looks like incense sticks which are placed near the deceased during the vigil. We don't know of any superstition regarding that; it's just inappropriate.