There are two things that bind any given branch of a constitutional government to the dictates of another branch:
- The dictates of the constitution itself.
- The will of the people.
The first one, however, has only the force that each branch and its constituent members give it. If the Executive branch collectively decides to selectively (or wholly) ignore the constitutional dictates of the judicial branch (as in your case), then the constitution itself has no force to stop the Executive branch. The branches willfully imposing upon themselves the dictates of the constitution, even when it seems inconvenient or undesirable, falls under the concept of "respect for the rule of law". The belief being that it is better to be guided by (democratic) laws and constitutions than to allow particular governments or individuals to dictate things according to their whims. Otherwise we end up with things like dictatorships, which have historically proven themselves to be undesirable for all but the few people in power (and even they sometimes meet an awful end).
This then pulls us into the second point, which is the will of the people. If one branch of a (democratic) government starts ignoring and disrespecting the rule of law, it then falls to the people to make them pay the consequences: demand rectifying legislation or other measures, elect new officials, recall existing ones, engage in protests, and in extreme situations outright rebellion. Of course, if the people by and large don't mind what's happening, or have too little power to effect change, then the offending branch can continue to do as it pleases.
China, for example, is considered by many, including its own people, to have a corrupt government. But the people are either too powerless or too unwilling to stop it. Keep in mind that before the current style of government the country was under significant duress from overpopulation, including widespread food shortages, and economic underdevelopment. This rendered many of the people desperate and willing to accept a certain degree of corruption and non-democratic rule provided the government solved and prevented such problems; it also led them to essentially accept the One Child policy. And for the most part they are credited for having done so and continuing to do so, and so the government continues largely unchallenged by its own people.*
*Reality is of course never quite so simple as to be boiled down to just a few sentences. But from my experiences with Chinese nationals, this is one of the major factors they point to.