Sure, phone surveys for political purposes (presidential approval ratings etc.) have to deal with that all of the time. There are methods for estimating non-response impact. [0] One method of
mitigating it that I've seen it to reach out again to non-responders. You then analyze
their results to see how they differ from the baseline responders to estimate the non-responder population. If there's little/no difference, you can be fairly confident the risk of bias is low. It's called non-response follow up, and is a pretty common method.
There's also literature that suggests that you don't discard outlier values in the actual responders as they may help approximate the non-responder population, i.e., the non-outliers represent typical responders while outliers are more likely to represent non-responders [1]
[0]https://www.warc.com/content/paywall/article/jar/research_no...
[1] https://bmcmedresmethodol.biomedcentral.com/articles/10.1186...