Firstly, what is awakening? There can be a lot of over-elaboration and magical thinking surrounding this question. The plain truth is that awakening is simply a fresh seeing or recognition of how things really are. A recognition that cuts so deep as to be better described as a paradigm shift.
So who or what has this recognition? Well, let's use the old ocean/wave analogy for a moment. The wave goes about its business believing that it is a wave. One day it comes to recognize that it is in fact not other than the ocean - the ocean is its source, power and essence. Now, from here it wouldn't be in any way accurate to say that the wave has awakened since the wave is without power, autonomy or agency. Instead, the awakening can be seen to be a play of the ocean.
So, the apparent entity does not awaken - but the pattern and process that is the mind-body organism is the mechanism through which a recognition occurs. In fact recognition only has relevance within the finite play of the organism. Beyond this play, the need for a recognition is without meaning.
You see, awakening or recognition could be said to be a corrective to a delusion. The delusion of separation is out of kilter with an underlying intuition of wholeness. This schism fuels certain psychological drives that eventually induce the spiritual quest towards completeness. Recognition simply reveals that completeness is and was already the case.