At Farnborough, we often got people who had been 'streamed' to Area Radar (NERL) originally, got chopped and were offered a post in NSL at an aerodrome. Course they only had an ADV/ADI rating so then (when and if they gained a C of C in the tower) they had to be sent on an APS course.
NATS (as far as I know) never 'chopped' a student in recent years (since about 1995) without giving them a second chance, even if it was just to offer them an ATSA post.
Different in the ATCO Cadet days, you never got a second chance; if you had been a assistant prior to getting an ATCO Cadet course, you were usually offered your old job back but if you were direct entry, you were usually chopped completely even if you had got one rating and that's where IAL (nowadays SERCO) and others got a lot of their controllers.