Fortunately, this type of issue is common enough that Google has established a method to prevent your clients from clicking on a search link that leads to a page that no longer exists.
When a user sends a parameter value, Google decides which URL to display based on the page that may contain maximum results.
Within the Google Search Console, you can request Google to totally ignore the paginated results and eliminate duplicate content, as well as missing pages.
IDX pages use a URL string of "&start=" to indicate the page of results. With this as the standard, we can tell Google how to treat each of these pages.
Log into Google Search Console and add "&start" as a parameter that affects pagination. Set the radio button to No URLs, to tell Google to not display any of the additional pages. Alternatively, you could set to show all or let Google decide.
Here is more documentation on the URL parameters tool from Google.