I know someone who had a very senior position (director level) at another airline.
Apart from travelling for work in F, he and his wife also had unlimited private travel in F. His children in J up to age 25.
But this was always a normal, booked seat, as if it were a commercial booking (if there was a seat for sale, he could book it) so it would not be clear to anyone but the cabin staff that he was 'different'.
After retirement, this situation continued for 5 years. Now it is down to two round trips per year on a space available basis 9and he has to pay the surcharge and taxes).
From what I read upthread (and that is the point of my response), I can't see how it works for EK staff with F privileges. Is it something like 'space available at T-24 or something like that? Guess it also depends on where in the pecking order you are....