From my knowledge of it, there is a core called the "Silver Cord" which connects you to your Physical body. Most people do say that they never see the cord, but it is possible for some to see the cord. Some people have said they saw it when the got scared or were frightened, such as a guidance back to their body.
And to answer another question, the cord itself cannot break. Although many people say it can. Astral Projection is a pretty cool thing, but you need to be careful while doing it. Be sure to keep calm and have positive thoughts, and make sure you have some kind of protection from demons around your body. People have said demons see the body as "vacant" and try to "possess" it.
Hope I helped.