There are employers our there that hire PhDs to do something that looks more or less like research. However, research positions for a single small topic of research are incredibly rare, and will usually be filled by hunting high-profile established researchers; a typical example would be computer security departments of big IT names. This happens when a company calculates that throwing large amounts of money at a big problem (or multiple related problems) is rational because the value of solving it is very large. In that case it is worth paying top salaries even for a small increase in the probability of success. If you are a PhD student, not on a "hot subject", and nobody contacted you (or one of your colleagues) after reading publications to fill such a position, your chances of finding one are basically zero.
The bulk of after-PhD industry R&D positions, from my experience (job-hunting and working in such for 2-3 years), require you to be somewhat flexible in your research topic. Of course this is extreme in smaller companies, where the "R&D department" can be one or two persons. Even in large companies you need some flexibility: my current employer has >100k employees, including ~3000 in entities dedicated solely to R&D, and my job title is "thermal transfer researcher"; yet, I regularly have to do material science, mechanics, electrical engineering, statistics, sometimes algorithms and even chemistry (yuck!). The ability to pick up quickly a basic understanding of a new topic is one of the big reasons the industry hires PhDs; if you do not you have the willingness to use that skill, I would avoid industry positions.
I expect this aspect of my experience to be quite universal due to the financial incentives at work. Both in industry and in academia, you get funding if someone who holds the purse is convinced that you spent well the previous round. In academia, funding committees care essentially about how many citations your papers get and in which journals you publish (maybe they should care about other things but that is another debate); they do not care about what your research is about. Working on topics where you are the best or the most interested in is often a near-optimal strategy under those incentives.
In the industry, good output means you solved someone's problem. The ability to do so is somewhat correlated to domain-specific technical skills but many considerations take precedence:
- sometimes, the actual solution to the problem is very different from the solution that was considered when funding occured, which determined who the task would be assigned to; yet re-assigning the task once the new solution is identified would be too expensive (in money, delay, or human resources)
- sometimes, someone close-by in the flowchart died or was run over by a bus, and managers cannot be too picky about who will finish the job they left;
- sometimes, the funder already worked with you, and your skillset is close enough that you are a safer bet than a top-notch technical expert that might be impossible to work with; or there is no such technical expert that the funder knows of.
