There can be no deal if both sides refuse to negotiate and seek a solution.
One side believes that letting go of their position means losing. In their view, there is nothing as valuable as the place that they have staked out. The other side believes they cannot accept that position, and so, they have reached a stalemate, which means both sides lose.
The other side believes they have to defend their position and anything that would change what they have laid out as necessary to a deal means losing. The first side cannot agree to those terms, and so there is no movement. Neither side gets what they want or need.
What both sides have done is cut themselves off from the possibility of collaboration in trying to find a solution in which both sides will benefit as much or more than the current position to which they are committed to now. The refusal to let go of your position long enough to explore other options is a kind of pig-headed devotion to how you achieve an outcome instead of a similar commitment to achieving the outcome itself. It also eliminates the exploration of new potential deals that create better outcome for both parties.
Not that it always works, but the person who is willing to be most vulnerable and suggest they are willing to explore new possibilities can break the logjam by going first, by suggesting they are willing to give up their current position to a seek a better position for both parties. Sometimes the outcomes of two parties are at such odds that there is no new possibilities because the outcomes are in conflict. But more often than not, there is a way for each party to work towards a solution where both parties find a position that is better than their original position, even if it takes work, and even if both have to give up their current demands.
If two parties both believe that the way they win is by ensuring the other party loses, then neither is bargaining in good faith, and they have cut themselves off from a deal that would better serve both of their longer term outcomes.