Whenever Zen Buddhist talks of 'emptiness', or 'no', they are essentially referring to dependent origination with the terminology as used by the Madhyamaka. As stated by Nagarjuna:
All dharmas that arise from causes and conditions,
I call them emptiness.
They are also provisional names,
And also the Middle Way.
What Nagarjuna is saying, is that because all dependent originated phenomenon are due to causes and conditions, by their very conditionality they are impermanent and without self. As stated by the Buddha.
"When this is, that is;
This arising, that arises;
When this is not, that is not;
This ceasing, that ceases."
Therefore because things are impermanent and without a true lasting self. He call them 'empty'.
So Huineng's famous stanza response to Shenxiu:
Our body is the Bodhi tree,
And our mind is like a bright mirror with stand,
Diligently we wipe them all the time,
And let no dust alight.
As Shenxiu indicates: we need to practice to cleanse ourselves of defilement craving, aversion and delusion as represented by the dust. This is reflected in the practice of mindful concentration (following monastic discipline and meditation) which can suppress the effects of our mental afflictions.
There is no Bodhi Tree
Nor the stand of a bright mirror,
Since all is void,
Where can the dust alight?
However Huineng using wisdom pointed out that in fact the body and mind are themselves dependently originated. That is they are caused and conditioned, impermanent and without self, so where are afflictions actually coming from?
The 'dust' themselves are dependently generated craving. This is the root source of suffering. As noted earlier, emptiness means impermanence and not self. The defilement has a condition for appearing, and when the condition is removed (through the application of wisdom), the defilement dissipate. The awareness of impermanence, selflessness and understanding of dependent origination is the tool for this. Of course that level of insight only comes with the practice of ethics and concentration. So Huineng is not denying the validity of what was said by Shenxiu, but that there is a deeper way of seeing things with wisdom.
Tozan said to his monks, "You monks should know there is an even
higher understanding in Buddhism." A monk stepped forward and asked,
"What is the higher Buddhism?" Tozan answered, "It is not Buddha."
So Tozan (Chan master Dongshan Liangjie) is pointing out that true wisdom is seeing emptiness, impermanence and selflessness even within the Buddha. That a Buddha is dependently originated too.
Ultimately Buddhism is still talking about dependent origination, impermanence, not self, suffering and the end of suffering.