I would think of a "case selection" as quant --> QUAL and I have a chapter on this design, along with several examples, in my book, Integrating Qualitative and Quantitative Research. You might also look at Teddlie & You (2007) on sampling in mixed methods research.

In general, I think of this design as widely used by not well recognized. In particular, qualitative researchers often made use of quantitative databases and other sources to help with purposive sampling, but they do not explicitly treat this as using mixed methods.

Thank you very much for your answer David L Morgan

That's very helpful. I will read your chapter with great interest!

I quite like the concept of a quantitative / qualitative continuum. This ResearchGate article has an effective diagram (figure 1) about different points along the continuum:

Bisman, J. (2010). Postpositivism and accounting research: A (personal) primer on critical realism. Australasian Accounting, Business and Finance Journal, 4(4), 3-25.

Article Postpositivism and Accounting Research : A (Personal) Primer...

Niglas, K. (2007). Introducing the quantitative-qualitative continuum: An alternative view on teaching research methods courses. Learning and teaching of research methods at university, 185-203. https://pdfs.semanticscholar.org/ba8d/21e6c7a48e1f1302f316661ff795aa1bd3a8.pdf

Newman, I., Benz, C. R., & Ridenour, C. S. (1998). Qualitative-quantitative research methodology: Exploring the interactive continuum. SIU Press.

https://ecommons.udayton.edu/cgi/viewcontent.cgi?article=1121&context=eda_fac_pub

Park, C. (2004). From qualitative to quantitative continuum: Exploring the possibility with the aid of CAQDAS (Nvivo 2). English Teaching, 59(4), 71-91.

http://kate.bada.cc/wp-content/uploads/2015/02/kate_59_4_4.pdf