Under the veil of ignorance, either the mind is unwittingly being determined or disturbed by the modifications of the mind, or the mind is aware of itself is being determined or disturbed by the modifications of the mind, however, it doesn't know how to be free from being determined or disturbed by the modifications of the mind via non-attachment.
If the mind knows what is non-attachment towards the modifications of the mind, and there's an effort coming from the mind to be performing an action or a practice of to be unattached, then this mind is practicing non-attachment towards the modifications of the mind, in order to be undetermined and undisturbed by the modifications of the mind, or the mind perception of names and forms that the mind perceives through the senses. There's still separateness between the mind and the practice and the object of the practice.
The action or practice of non-attachment comes to an end, when it is no longer an action or practice that requires certain effort from a practitioner, upon the realization of selflessness, non-separateness, or oneness. There's no separateness between the practitioner and the practice and the object of the practice.
There's no need an effort to be not attaching towards anything, under the absence of ignorance and egoism, where all and everything, the perceiver and the perceived, the subject and the object, are all selfless, and are subject to selfless impermanent changes.
The mind that is void of suffering doesn't need to be free from suffering. What is non-attachment, who is non-attaching, what is to be unattached, in silence, in selflessness?
Before that, the mind that still perceives separateness and duality under the veil of ignorance, that still perceives doubt and suffering, and is still in searching for the end of suffering, will still have to make an effort of keep practicing detachment and non-attachment.