Do some texts say about what is happening with consciousness/mind which reaches liberation?
There are different levels of enlightenment and liberation. These follow two (or three or four) paths - Hinayana, Mahayana, Vajrayana and Dzogchen. The distinction between Hinayana and the other paths is purely motivation - does one seek liberation for oneself alone or does one seek liberation for all beings? The differences between the Mahayana, Vajrayana and Dzogchen paths are all method (how and what one applies to follow the path).
Since the actual difference between Hinayana and Mahayana (with Vajrayana and Dzogchen subsumed into Mahayana) is the motivation, one can follow the methods of the Mahayana paths and still get the Hinayana result of liberation for oneself if that is one's actual motivation.
On the Hinayana path, the emphasis is in defeating mental defilements. On the Mahayana path, the emphasis is developing the intention to attain Enlightenment for all beings and accumulating merit and wisdom.
There are different realizations (the results of the training) along the way.
We can gloss enlightenment as being the purification of the mind (except that isn't really correct and that's not all there is). Complete Enlightenment is the complete purification of all defilements (negativities) and the the complete development of all positive qualities and spiritual power.
For example, Shakyamuni
He achieved enlightenment,he died and now what?
He sees us?
Or hears us?
Can respond to our requests?
The Buddha's are said to respond to us constantly, non-referentially showering blessings. These are blocked by our lack of faith and karmic obscurations. So we have to get rid of a lack of faith and reduce (hopefully eliminate) our karmic obscurations. Thus Buddhists universally take refuge and near universally engage in some form of compassion and/or lovingkindness training.
_________________Kirt's Tibetan Translation Notes
"Only you can make your mind beautiful."
HH Chetsang Rinpoche