Yes, but the requirement is not restricted to just hospitals.
See:
640.3(A) Abandoned Audio Distribution Cable.
725.3(B) Abandoned CL2, CL3 and PLTC Cables.
820.3 Abandoned Coaxial Cable.
800.52(B) Abandoned Communication Cable.
760.3(A) Abandoned Fire Alarm Cable.
770.3(A) Abandoned Optical Fiber Cable.