In The Projection of the Astral Body by Sylvan Muldoon & Hereward Carrington, and in Astral Dynamics by Robert Bruce as well as a number of other OBE/AP books the "cord" is mentioned. It is sometimes referred to as the "astral cord", "silver cord" or even the "astral cable".
Bruce defines it as "the two-way energetic linkage connecting the physical/etheric body with its projected double". Muldoon & Carrington state: "..the astral cord is an elastic-like structure, connecting the astral body with the physical.." and "This vital structure is composed, so far as I am able to see, of the same material, or essense as the astral body itself."
According to what information I have come across, the only way the cord separates is at death of the physical body. That is, nothing can "cut it" but physical death itself.
Very best,
What is the cord attached to you in the Astral Plane I've heard of?
What happens if something cut it?[?]