There is a chance that one effect might be that the driver observed the Overheating indicator lamp or gauge and stopped driving it while he puzzled out what the problem was.
For a while the oil would help carry away heat. Then it would burn and smoke.
If it`s a Vauxhall Astra with GM engine ........even a brief overheat can stuff the head gasket.......there`s one on my drive that used to be our good car service history as long as your arm ........now it`s scrap