How could two waves on a rope interfere so the rope does not move at all?

This can happen in the case of destructive interference. When two waves on the rope, having same wavelength interfere in such a manner that a particle is on the crest of one wave and the trough of another wave, then both waves will cancel each other out, creating a node, such that the particle does not move at all. Hence, the rope will also remain constant if both waves interfere in this manner