Job applications typically require the applicant to describe their research interests (research statements). Would it be a worry that an applicant's work-in-progress/current interests would inspire similar works from the reviewer's side? If so, is it wise to describe these ideas, or better avoid doing so?
Regarding the application letter:
The aim of an application letter should be an invitation to a job interview. Keep in mind that an employer (within and outside academia) wants you to work on their problems.
You could try to spark their interest by stating something like "I have worked (are currently working on) some original solutions for the XYZ problem.", without going into details. When they are interested in the details, they can ask you in the interview.
Try to avoid elaborate descriptions of your current ideas. Not so much to prevent anyone from stealing them, but rather because they tend to distract from the primary goal of an application letter: to get invited for the interview. Just sufficient information to make them curious would be perfect.
Regarding the application interview and/or research statement:
When your current work is only partially related to PI's work it is not necessary or desirable to go into the details, and there is little chance of anyone stealing your ideas anyway.
When there is significant overlap, it might be wise to put a preliminary paper online (e.g. on Arxiv). In that way you can claim the ideas to be yours, and freely discuss them.