I get what your employers are saying, but a bit over the top if you ask me.
The employers have no way of knowing if the non-EEA citizen using EU free movement to be in the UK, is in the UK legally. The employer was correct in pointing out it is these employees sole responsibilty to ensure they can still work in the UK.
If their EEA citizen sponsor ceases to be a
qualified person then they and all their Family Members, lose the right to reside in the UK.
An RC is only given as their EEA citizen sponsor was being a
qualified person at that time and is in expectation that their EEA citizen will continue to exercise treaty rights (be a qualified person at all times). An RC becomes an invalid in their EEA citizen sponsor ceases to be a
qualified person. The end date on an RC doesn't mean a lot as it is not like a UK visa.
If the non-EEA citizen fails to telll their employer that they thay have lost their right to reside and work in the UK (as their EEA citizen sponsor has stopped being a qualified person) then how can the employer know this?
With illegal working being made a criminal offence last year, for the employer and the worker, I don't blame the employers for protecting themselves by sending out these letters.