When a researcher begins with a specific case or participant, and then applies those findings to subsequent participants in order to develop a theory, they are?

They are "utilizing a cross-case method approach and grounded theory".

Grounded Theory is an inductive strategy. Albeit numerous call Grounded Theory a subjective strategy, it isn't. It is a general technique. It is the methodical age of hypothesis from efficient research. It is an arrangement of thorough research strategies prompting the development of applied classifications.