Let’s say you’re doing a sociological experiment in which you track the voting record of a certain demographic.
You start with 10,000 people.
You are still tracking them in the year 2030. By then, however, the population size has fallen to 5000 people - the other half died and therefore cannot vote.
What is the sample size?
Hypothetical #2:
You’re still tracking the same demographic in the year 2060. By then, 9999 members of the original population have died.
Can you still report a meaningful result for year 2060?
You’re describing a longitudinal study with death. It’s not so simple to analyze as just fixing a single sample size at the end. Google for that phrase to get the literature.
Longitudinal studies are found everywhere in medicine and biology. They are the gold standard of health and nutrition research. Take a look at the nurse’s health study, one of the most important sources of information about health in everyday life as a prime example.
A longitudinal study simply means studying the same group of people more than one time. If I asked you questions this week and again next week, that would count as a longitudinal study. (The converse is a cross-sectional survey, in which you only survey people once.)
One of the difficulties with longitudinal studies that occur over a longer period of time is that people withdraw from the study for many reasons other than death. There are statistical techniques to deal with bias due to attrition. Thankfully, public use datasets typically come with different weights to use based on which wave(s) of the study you’re using, so I’ve never needed to become especially familiar with those techniques!
If you’re interested in longitudinal surveys in the social sciences in the US, you could look at the National Longitudinal Studies or the http://psidonline.isr.umich.edu/. In the UK, there is the British Cohort Study, which has followed everyone born in a certain week in 1970 over the course of their lives. There are a couple of others with older and younger cohorts. I imagine that the websites for these studies will have information about the statistical techniques used to deal with attrition.
Longitudinal surveys are really useful for getting closer to understanding causality than a cross-sectional survey will do, but they are a lot of work.
You might also find survival analysis interesting. Not the same thing as what you are talking about, but along the same lines. Make sure you read the part about “censoring”.