Eligibility to vote in the US is affected by two federal laws, NVRA and HAVA. Under NVRA, voters can be purged from the rolls under a variety of complicated criteria and processes, with the law setting only general guidelines but leaving the specifics up to the states. A common criterion is that voters are removed if they haven't voted for a long time and also fail to respond to mail at their registered address. There is also a program called ERIC that involves checking against government databases such as DMV, postal records, and social security records. HAVA, passed as a response to problems with the 2000 election, provides a safeguard against the disenfranchisement of voters, who are entitled to a provisional ballot if they show up in person but are not found on the rolls, but I think state laws typically say that the provisional ballot should be rejected if the voter is not actually registered.
A right-wing group called Judicial Watch has successfully sued in the past to get rolls more aggressively purged, which, e.g., resulted in the removal of 1.5 million names from the rolls in LA county. They are currently suing three Democratic-leaning suburban Philadelphia counties to get them to remove 800,000 names from their rolls.
In principle, purging could reduce the number of "false positives," i.e., the number of votes cast that should not have legally been allowed, but at the expense of some number of "false negatives," i.e., cases where a person is not allowed to vote only because of factors such as their inattention to mail or to factors beyond their control. This question is about the false negative rate.
Question: Are there any careful independent, nonpartisan studies that have been able to estimate the false-negative rate in past elections?
I may be wrong, but I would suspect that the false-negative rate would be fairly low. This would be because (a) many removals are accurate; (b) a lot of people who are removed inaccurately would never have voted (failure to vote in the past being one of the criteria for removal); (c) people who request a mail ballot in a timely manner might find out about the problem in time to fix it; (d) people who attempt to vote in person can cast provisional ballots, although I'm guessing that the ballot would then be rejected under most states' laws; (e) 15 states offer same-day registration.
But maybe there are specific states and counties that did their purging very incompetently or with the intention of voter suppression, and therefore did have a lot of false negatives. If so, is there any quantitative documentation of this?
The best nonpartisan academic analysis I've found was an MIT paper by Pettigrew, but it just tries to estimate the accuracy of purges, not their actual effect on elections.
[EDIT] As a rough nationwide estimate of the impact, we could take the number of provisional ballots that were rejected because the voter was not registered in their state. In 2018, this was about 0.1% of the ballots cast, which would suggest that the quantitative effect on elections was small. However, there could be certain states or counties where the percentage was much higher. Both the prevalence of provisional ballots and the rejection rate vary greatly across jurisdictions. There is also no guarantee that people who have been purged were offered the option of casting a provisional ballot or decided to take that option.