It is understood in mathematical statistics that a sample (as in sampling distribution) may very well contain repeatedly the same item/subject.
In practice though, it would never occur to someone conducting an experiment (e.g. in human sciences studies) to take into account the same subject twice. Samples are made
- by taking the first people who agree to take the tests and look random enough (e.g. using quota sampling).
- by taking the only $12$ people living in your country who fit the requirements of the study (e.g. when you're conducting research on a rare disease) (and yes, $12$ is ridiculously small but that's still what is being done when no more subjects are available).
In what situations can this habit turn out to be really bad - induce a huge bias on the results?
What seems clear to me is that if the total population is large enough, then it shouldn't matter too much, since samples with repeats are quite unlikely to occur and don't weigh much in the sampling distribution. When the total population is small though, it feels like we're more likely to miss something.