This answer is in the context of the Tibetan Gelug School and is taught in modern Buddhist Monasteries of this tradition.
Uncompounded space (as opposed to the usual idea of space) is a permanent phenomenon. This is the standard example of an existing thing that is permanent. Like emptiness, uncompounded space is taught to be a non-affirming negation. So what is uncompounded space? First, we have to understand what compounded space is...
Compounded space is the vacuum between material things. Take two material objects (made of matter) that are spacelike separated. This means not only do they not occupy the same space, but that they have a vacuity between them. Imagine they are placed in the void of deep space with a meter of distance between them. In this meter of distance between them, there is no air, there are no molecules, no matter. This is what is meant by compounded space.
Uncompounded space is the complete absence of obstructive contact. Those two things we imagined above are spacelike separated and sitting in a void. They have no contact with anything. They have a complete absence of obstructive contact. They are sitting, if you like, in uncompounded space.
This is thought of as a permanent phenomenon and not dependent on causes and conditions. How can it be said to be independent of causes and conditions? Unlike compounded space, it does not rely upon matter. Whether there is something sitting in uncompounded space or not, the mere absence of obstructive contact remains. It is unproduced.
Objection! Doesn't this mean that uncompounded space contains a self? Doesn't it mean that it is inherently existent?
Answer... No, because it is a mere non-affirming negation. It is the mere lack of obstruction. No matter how hard you look "inside" of uncompounded space you will find nothing. There is no inherently existent self in uncompounded space that can be found. This is what is meant by a non-affirming negation. There is nothing left whatsoever to be reified.
Objection! But isn't uncompounded space an independent phenomena?
Answer... No, it is dependent upon name and designation. It is empty of inherent existence just like all phenomena.