‘Sankhata’ means constructed, made, prepared, built, or formed. In the early Buddhist context, it refers specifically to the world that is constructed through our choices and craving in the cycle of rebirth. The related term ‘sankhāra’ or verb ‘(abhi)sankharoti,’ refer to volitions or intentions that are expressed in action and propel our consciousness forward into more constructed states of being that are shaped by those intentional activities. The end of ‘building’ worlds, of constructed or formed states, is the cessation of this process of rebirth. This is called ‘asankhata,’ meaning freedom from, the absence of, the end of, or the non-doing of what is ‘sankhata.’ It is simply a negation of that first state — rebirths made from ignorant choices and craving. So it doesn’t really make sense for there to be a “third” option.
Say we have an apple. And we have the option to keep the apple, or remove the apple. The idea of a ‘third’ option is irrelevant here. Trading the apple for an orange would still be ‘removing the apple,’ and adding another thing to it is keeping the apple. Apologies for the crude and imperfect analogy.
The key is that the Buddha’s insight specifically was that all existence is constructed and built up, liable to fall apart. Everything is an apple, and removing the apple is the only other option. The Buddha’s insight is that there is no escape in some kind of un-conditioned existence. Rather, he shifted the emphasis to the ending of the problem as being the solution, not some other solution that is after or beyond the ending of the problem. The end of suffering itself is the happiness.