Fear is real. Students may feel afraid that they are going to be humiliated, or that their assertiveness will result in abuse by their classmates. They may even fear adults.
Some teachers believe that the way to deal with such fear is to create incremental steps which allow students to make conservative choices. Modest choices which are not really threatening. The logic is that over time frightened students will see that participation is fun and will want to take more risks.
Wrong! That only proves that they were reluctant deadbeats or indolent wannabe royalty. If students are afraid, the teacher should try to create exercises which feel really scary. The teacher should simultaneously model supportive behavior. Teachers should communicate that anything that goes wrong in the class is the teacher's fault! I tell students "Blame me!" Give students honest feedback and they will trust you. Make it clear that you will take responsibility for anything that goes wrong and they will take risks.
Activities which seem frightening at the beginning become thrilling when they are experienced with out actual negative consequences. (That's how I got addicted to horror movies.) Children who are taught to take risks grow into spontaneous confident adults. Students taught to make conservative choices feel stifled and repressed.
Reluctant deadbeats are usually suffering from lack of sleep or bad nutrition (either too much food or not enough of the right foods.) These problems should be dealt with outside of class.
Indolent wannabe royalty should be given maximum responsibility, preferably control over life and death! Address such students by their proper titles; Prince Zhang, Princess Alia, Queen of the Elves. Allow them to pick the next "volunteer!"
That usually works, but sometimes a very skilled princess will pretend that they are afraid to speak. In that case pretend that they gestured with their eyes at some other student who wasn't looking and call that student up. If they are a true queen they will become indignant and declare that they did not, and would not have made such a choice. You have won. Now all the other students know they are not shy.
[I got this line of thinking from Keith Johnstone who wrote Impro, which is the best book on teaching I have ever read. It claims to be about teaching theater but all the principles are universal.]