Running Dijkstra on particular graph with negative weight
The shortest path tree of Dijkstra will set root as $S$ then it first selects the $Y$ with weight 8. Then it will look at the shortest distance of all the neighbor's of the tree. There will be two candidates $X$ and $Z$. It will choose $X$ since the distance is 10. Then finally, it will choose $Z$ with distance 11. 

The Dijkstra's, as stated, cannot work correctly on graphs with negative weights.

The problem is that it is a greedy algorithm and once it finds the shortest path for a node it is not re-evaluating for any other possibilities may occur in the future. This is not possible if the graph has not negative weights.