Rotor-wing question

Hello all,

This is my first time posting here, but I figured maybe you all could
help me out with a question that has been nagging at me for quite a
while. Forgive me if this seems like a stupid question.

Here goes:

Does a helicopter, without lateral movement, have the ability to fly
down, or does it merely stop holding itself up?

I don't know if that makes sense, but I don't know of a better way to
word the question. I would be happy to clarify if necessary, but i
don't know what to add.