This process is specified in DO-178C. It is a kind of communication process with Certification Authority. It is very important for suppliers to get a good results. I’ve never experienced about type certification or airworthiness certification, but I think that I can imagine the procedure because there are published document.
Though it is natural to think, applicant has to submit safety plan to certification body and it can be proceed if the plan is approved by certification authority.
It would be ridiculous if applicant submit safety plan in the middle of the project. What if the plan is rejected? Everything they have done so far must be dumped.
Unfortunately this process is not defined in the automotive, but it also essential for supplier. Competent OEM may have a detailed process for audit and assessment.
You can also refer a book, “Developing Safety-Critical Software(DO-178C)” in chapter 12