Suppose you want to collect some kind of data from a population, but people vary widely in their willingness to provide the data (eg maybe you want to conduct a 30 minute phone survey but some people really dislike phone calls or have much higher hourly wages this funges against).

One thing you could do is offer to pay everyone $X$ dollars for data collection. But this will only capture the people whose cost of providing data is below $X$, which will distort your sample.

Here's another proposal: ask everyone for their fair price to provide the data. If they quote you $Y$, pay them $2Y$ to collect the data with probability ${\left(\frac{X}{2Y}\right)}^2$, or $X$ with certainty if they quote you a value less than $X/2$. (If your RNG doesn't return yes, do nothing.) Then upweight the data from your randomly-chosen respondents in inverse proportion to the odds that they were selected. You can do a bit of calculus to see that this scheme incentivizes respondents to quote their fair value, and will provide an expected surplus of $max(X^2/4Y,X-Y)$ dollars to a respondent who disvalues providing data at $Y$.

Now you have an unbiased sample of your population and you'll pay at most $NX$ dollars in expectation if you reach out to $N$ people. The cost is that you'll have a noisier sample of the high-reluctance population, but that's a lot better than definitely having none of that population in your study.