Pierre Levegh got close, but the engine let him down. I don't think anyone has ever finished the race driving solo.
Pierre Levegh was an alias, his real name was Pierre Bouillon IIRC. Levegh was an anagram of Velghe, the name of his uncle who competed in early long distance races.
Levegh drove for about 23 hours before a crank broke IIRC, it was this level of commitment that got him the drive for Mercedes in 1955.
I'd recommend reading 'Managing A Legend: Stirling Mos, Ken Gregory and the British Racing Partnership', pages 154-157 for an account of the 1955 accident.
It's written by Robert Edwardes and is well worth reading simply for its own sake.
A very good book.