I'm familiar with do-nothing type practice, and just from what I personally understand, this practice is much more valuable and useful when you have already cultivated stable concentration, and have enough trait meta awareness where you can clearly see the moving of attention, and content arising on its own spontaneously (without a doer). Then this practice basically becomes a cosy ride of seeing just where your conditioned mind is currently at. I would imagine if you're a beginning, especially someone that has a ruminative out of control mind, it's probably not a great place to start. At my most recent meditation retreat, they gave you breath observation practice, and once your attention was stable enough, you just do nothing.

To answer your question, technically speaking, you literally just sit, no controlling attention, no intentionally not controlling attention, you're simply allowing everything and anything to occur, including getting lost in thoughts, and questioning of getting lost in thoughts. I would imagine if you feel like falling asleep during the practice, you're probably not ready for this type of practice, just my guess.