Resampling small datasets - Issue of overcounting? Hypothetical situation here, as techniques like bootstrapping often fail for very small datasets.
Taking bootstrapping as an example nonetheless. we can easily compute the number of possible bootstrap (re)samples.
A nice answer is given by @whuber here:
Amount of Possible Bootstrap Samples
Suppose for a moment that bootstrapping is perfectly valid for low sample sizes. Now, say we have $n = 5$. From the posted solution above, it is found that there are a total of 126 possible boostrap resamples that can be drawn.
In bootstrapping, we usually take a large number of replications (10000 for instance). Taking this many replicates for such a small dataset, like the one above, seems bizarre, since resamples will be counted multiple times.
Question: Does this really matter? If yes. what is the effect on inference?

When bootstrapping, we are assuming that the sample is representative of the population.
The whole purpose of bootstrapping is to estimate a sampling distribution and infer the likely standard errors and confidence intervals for the population as a whole.
However, the issue with small sample sizes is that bias is more likely to exist relative to large samples - and (contrary to popular belief) bootstrapping does not fix this bias or remedy the issue of small sample sizes.
For instance, suppose one were to roll a dice five times. The numbers 4, 5, 6, 6, 6 are obtained, for an average of 5.4.
If one were to roll a dice a hundred times, an average closer to 3.5 could be expected - which is the theoretical mean.
However, small samples have a higher chance of deviating significantly from the population mean and so bootstrap sampling will not remedy this by virtue of simply generating more observations.
