The closing date for applying to the EU settlement scheme is the 30th of June 2021 but this includes a grace period of half a year for individuals who forgot to send in their applications. Vulnerability is also given consideration in the EU settlement application, so those who are vulnerable are also allowed to take advantage of the grace period.
This means that every EU national in the UK should have submitted an EU settlement application, either for EU settled status or for pre-settled status, by this date.