It is necessary to specify some methodological aspects.
In qualitative research there is a difference between the methodological design and the technique to extract the information.
By referring case studies, it refers to the methodological design that guides your research. The case studies are applied in different aspects, for example: very atypical cases, or cases differentiated from the rest, or cases that behave differently from the theory. Problems such as how. How do families survive in marginal areas with incomes well below the cost of the basic food basket? What are the psychosocial barriers faced by women who succeed in politics?
So the first step is to specify your case study, depending on what research problem and within that problem identify cases worthy of in-depth studies.
But when you refer to focus groups, you have to be careful, because it is a technique within qualitative research. The case studies are supported technically in the strong ethnographic work and in-depth interviews with a phenomenological approach.
In case you want to use the focus group within a case study thesis. It can be as a complement to the information you get from the case itself.
On the other hand if you have several subjects that make up the case study, I do not recommend making a focus group with them. In that sense, it is best to triangulate the information among all the subjects that make up your case study.
There are essentially three ways to select a focus group: pre existing, common interest or stratified. Pre existing already know each other, common interest share a common interest related to the topic being discussed in the focus group, statified are randomly selected but represent characteristics of the general population (e.g. gender and age distribution). There are pros and cons with each. One approach might be more appropriate for your context.
In line with Montenegro , if your methodological frame is case study , I think you do not need to go with FGD. Rather , having voices from various segments/strata of the informants may be more desirable in your case. Instead of doing triangulation , giving space for plural voice in their respective context will also be helpful.
It would help to know more about what you mean by "case study." In particular, as Peter Samuels says, it makes a difference if there are pre-existing relationships among the participants, because this raises an ethical issue. When focus groups are conducted with strangers, what the participants say to each other is unlikely to have any lasting impacts, but you cannot protect the privacy of what is said in the groups if the participants have ongoing relationships.
Beyond that, the most basic criteria for focus groups are that the participants should at a minimum feel comfortable talking about the topic with each other, and preferably should be interested in what each other has to say about the topic.
One option is to "segment" the participants into homogeneous groups, to maximize their shared interests within groups while creating interesting comparisons between groups. Note that "homogeneous" means how the participants are connected to the topic, not similarity of demographic characteristics.
As David said, first thing you have to identify what type of case study you are following to implement your research. Case study is defined as a methodology (Creswell 2007) or a research strategy (Yin 2013) or 'a choice of what to be studied’ (Stake 2005: 443). Each of type of case study leads to different ways of selecting your sample.
For instance, for Yin, you have to design your case study as a single case study or multiple case study (various cases). If you want to study further within each case (i.e., investigating sub-units of each case) then you should choose an embedded single case study or an embedded multiple case study.
Let us take a look at an embedded single case study. There are three levels to sample. For instance, your case is a city, then:
Context of the case (anything outside the case making its context): is the socio-economic and political environment of the region, state and country of the city.
The case itself: the city
Sub-units of the case: any parts of the city (spatial areas or groups or organisations depending on what you are focusing on).
If you want to apply focus group, then you have to identify which level you want to study. Focus group with context, or the case or sub-units.
Focus group is a data collection technique. It is suitable for collecting data from a number of people who do not have much time for individual interviews, and are temporary gathering. You have to make clear why focus groups are better individual interviews, documentary analysis, and observation.
There are many rules and techniques to facilitate a focus group. You can refer to a great book by Richard A. Krueger and Mary Anne Casey - this is a very useful guide.
Although, the question seems a month old and many people have already responded, yet, I think I can add something. As far I understand, you want to know the method of selection of participants for your case study. Well, to me, you can definitely use FGD for the case study design. For the selection of the participant, you just need to identify people who best represent your case and you can do it at your convenience. This process cannot and should not be random. It should be based upon the idea of representation. If, as a researcher, you find that your FGD participants have the characteristics required for the case, you can select them. As far as the number of participants is concerned, you can select as many as 14-15 or in other words as many as you can handle simultaneously. Furthermore, you can go for as many sessions as you deem fit. But, I think the information in a group starts saturating after 3-4 sessions.