They did not. Or at least there is no proof that the StB faked Martin Šmíd's death in order to achieve political change in Czechoslovakia. Although there are several elements of the incident that are at best uncertain, what evidence there is, coupled with the results of the official investigation, suggests that it is nothing more than a conspiracy theory.

There are two parts to this story. One is the fictitious death of Martin Šmíd, the other are the ex post facto claims that it was an StB plot. The former is perhaps less clear. Drahomíra Dražská was the person responsible for starting the rumour that a student had died during the November 17 demonstrations. To this day we only have her own words as to the motivation and reasons.

Dražská, who worked at a students' dormitory, has on several occasions stated that she had not acted in any official capacity and she had denied that the StB were in any way involved. Apparently she acted out of frustration and anger at being beaten by the police earlier that day.

Through various channels Dražská's claim made its way to dissident leader Petr Uhl, and through him it reached the rest of the world. But as everyone would soon find out, no Martin Šmíd died on that day and the opposition was quickly forced to deny their previous claims. In fact, the authorities became involved and Uhl and others were to be arrested for spreading false rumours and panic. Which also adds even more doubts to the second part of the story, the StB claims.

A junior lieutenant in the secret police, Ludvík Zifčák was indeed an undercover operative present at the protest. His mission was to infiltrate the anti-communist opposition posing as Milan Růžička. Following the Velvet Revolution, he would go on and make several bold claims some of which you mention in your post: Dražská was his co-worker, the whole thing was a secret operation backed by the Soviet Union, and its aim was replacing the communist leadership but not the regime as a whole.

However, he is considered highly unreliable at best. An investigation by the Czechoslovak parliament (in Czech) had found that there was no connection between Zifčák – an inexperienced, young officer – and Dražská, and that his 'death' was just an accident. Eyewitness reports and medical records say that he was hit by a police officer, and that he later lost consciousness in the middle of a crowd, hence the body on the ground. This version is also supported by his apparent confusion after he had awakened, and the StB being unaware of one of their agents being transported by ambulance.

Perhaps most importantly, the fact that Zifčák continued his undercover work as Růžička following the events of November 17, including further appearances at protests and demonstrations, is in direct contradiction to the notion that he was supposed to play the part of a dead student, and strongly suggests that his words about a conspiracy are just fabrications.

The actions and involvement of the communist regime during the Velvet Revolution are by no means perfectly documented. Even this fake death retains its share of unanswered questions. However, apart from the words of a bitter old communist, there is pretty much nothing to prove this particular conspiracy theory.