I believe it may help to clarify a few points about Buddhist thought. When using the term self existent, what is being referred to is an object that exists from its own side.
An easy example is that of a plant. If a plant were to 'exist' (keep in mind that here we mean independent inherent existence) it would have to basically be an island onto itself. However, this is not how a plant comes to 'be'. It is obvious that a plant relies on a set of causes and conditions. For example, it requires the sunlight, water, nutrients in the soil, and seed, and so forth. With all these conditions and causes in place, the thing we label a plant comes to 'be'.
Now we must be careful. In Buddhist thought there are two levels of truth to consider. Relative and ultimate truth. Relative, or conventional, truth is that which we experience in samsara, ordinary subject/object thought/experience. A conventional truth would be like the wetness of water, its a conventional property of what we label water. Another conventional truth, in Buddhist thought, would be the law of cause and effect, karma.
Generally speaking, the conventional truths are the ways that things appear to us in conventional reality, this is by a coming together or causes and conditions as described in the plant example.
The level of ultimate truth concerns the ultimate nature of phenomenon. At this level, the ultimate truth of ANY object is sunyata. This word is often translated as emptiness, voidness, sometimes even spaciousness or openness.
These two truths, the conventional and ultimate, can be seen as two sides to one coin. Lets take the example of a table. Conventionally, a table arises on dependence with causes and conditions. The material its made out of, the shape its been given, its texture and so forth. This collection is then labeled by the mind as a 'table'. In this sense it 'exists'....but when Buddhists say exists they typically mean exists independently from its own side, which the table clearly does not.
The other side of this 'table coin' is the ultimate. Ultimately the table is empty. In particular, it is empty of any independently inherently existent 'self'. This understanding of emptiness is of course conceptual, but in Buddhist thought this conceptual understanding can help lead to nonconceptual realization of emptiness, which leads to Buddhahood.