How to write research proposal without the risk of getting my idea stolen I am applying to some PhD programs this year. For some programs they require a research proposal - and this creates a dilemma for me. The more detailed the proposal is, the higher chance I get into the program but also the higher the risk that my idea is stolen. What can I do in this situation?
Thank you!
Yes, this is a known issue.  What you said is perfectly true -- a vague proposal will probably be rejected, a well elaborated proposal can potentially be stolen.
The situation is very similar with job applications, where applicants are asked to produce a research plan for the next 3 years, and members of the recruitment panel can be more excited with the elements of the proposal than with hiring an applicant. Speaking from personal experience, this puts applicant in a frustrating position.
There is no ideal solution for the applicant. However, the following helps:

Remain active and productive in research as much as possible and try to stay ahead of the crowd in your own field. If it is clear from your proposal that you are the best person who has the right skills to get the project done, then it is more likely that people will want to have you onboard.
Don't put all your eggs in one basket. Apply to several places quickly and move forward with your research at the same time. Even if someone decides to steal your idea, they won't be able to implement and publish it overnight. Use your time effectively and stay ahead of possible competition by moving faster than your competitors.
If possible, try to discuss the proposal informally with your potential supervisor first, and see how interested she or he is, and whether she/he would like to contribute additional ideas or details.