Here's what Augustine has to say, specifically thinking about the question: can we desire nothingness? Or non-existence? Doesn't someone's suicide show that we can desire nothingness for ourselves? Augustine says no.
"Someone who believes that after death he will not exist is driven by his unbearable troubles to desire death with all his heart; he chooses death and takes hold of it. His opinion is completely false, but his feeling is simply a natural desire for peace. And something that has peace is not nothing; indeed, it is greater than something that is restless. For restlessness generates one conflicting passion after another, whereas peace has the constancy that is the most conspicuous characteristic of Being.
So the will's desire for death is not a desire for nonexistence but a desire for peace. When someone wrongly believes that he will not exist, he desires by nature to be at peace; that is, he desires to exist in a higher degree. Therefore, just as no one can desire not to exist, no one ought to be ungrateful to the goodness of the Creator for the fact that he exists." (On Free Choice of the Will, Book 3.8)
What's the point? It's impossible to desire non-existence. What someone really desires is peace, an end to the restlessness that characterizes our sinful state apart from God. To desire peace is to desire God, who is true peace and our true end. So even the act of someone who despairs and takes their own life reveals that humans inescapably desire God.