One of the most famous examples of this was Derek Warwick running second in the Toleman at Brands Hatch in 1982. They claimed he had a driveshaft failure after he retired 40-odd laps in.
The advantages of this kind of strategy were tied in very closely with exposure for sponsors. At a time when not every race was televised live it guaranteed that Toleman – a British team – would get a lot of camera time in one of the few races that was shown live – the British Grand Prix.
There are other reasons why it wouldn’t work so well today. Reliability is far better and the performance advantage you need over another car to overtake it is much higher. Also consider that it takes until almost the end of the race for the likes of Virgin at Lotus to lap at the pace the leaders were doing at the start. See here: Italian Grand Prix fastest laps
There’s quite a lot on it in a recent book about Toleman by Christopher Hilton. According to him Rory Byrne was in on the plan as was Pat Symonds who apparently disapproved of it – apparently 26 years later he was willing to tolerate much worse things. Hunt out a copy of “The Toleman Story” for more.