Best way to rig a wire attached to a character

Hello,

I have a concept character rigged in Blender. I added some stuff to him, and in this stuff there is a blood bag attached to his body. The perfusion is going along the body to his arm, to his vein, I done a curve representating the wire making the connection.

My character is rigged (character creator, so he has a default rig). What would be the best way to make the blood wire follow nicely the movements of the rig / character (body and arm) ?

I never went in that situation
Thanks by advance for any tip

A modifier that can be attached using the Surface Deform modifier but works on the mesh.

Surface deform modifier as suggested by @oo_1942
If not, you can use the Data transfer modifier. And tranafer the vertex group data (the weight painting)
And add an armature modifier to it too.
P.s: apply the data transfer modifier