There are still jobs like that in the non-Agile world of business application, mainly in government I think (at least here in Europe). The position is called "system analyst" (sometimes also "business analyst", but that is likely to include more fluff). It involves writing down system specification, which includes detailed requirements, user's interactions with the system (use cases), the data model etc. The other part of the job is talking to developers while they're developing the system and testing their work(making sure there are no bugs and they they understood the specs correctly) after they're done.

It's not a bad job, definitely less headaches than coding IMO. The downside is that you need to deal with business people more (can be an plus for some people), and mainly that it's just not that common any more in the post-agile world. Also usually pays less than development.