I've found a method to do it. It's not perfect but it works :). It uses a Particle Instance Modifier.
Add a Cube (place its origin point in the same place as emitter's origin point). Scale it along the Z axis, then Subdivide, so it has the same number of loop cuts as the number of segments of your hair particles. Go to Object Mode and apply its transformations (Ctrl+A).
Go to Modifiers header and give it a Particle Instance Modifier. Enable the modifier's settings as pictured below.
It may not work properly though. If something's wrong just rotate your Cube 90 degress on the X axis (or Y, or Z, depending on your situation).
Now add an object which will be following your strands and rotate it perpendicular to your Cube. Select it, then the Cube and enter the Edit Mode. Select the opposite 3 vertices, as pictured below and press Ctrl+P-->Make Vertex Parent.
Go to Object Mode and place the following object (Torus in this case) wherever you want. Select a Cube and move it to another layer to see only the hair particles.
You may precisely parent any object to a chosen strand's segment. In Edit Mode select any vertices, then enable an option as pictured below (marked in red) to see where their location on the instance is.
Add a new object and parent it to selected vertices.
Then place it on a proper segment's location.
Now the object copies the location of the strand's segment.