Green’s Dictionary of Slang

undertaker’s job n.

[SE undertaker + job n.2 ]

1. (orig. Aus.) a hopeless proposition; thus ‘dead’.

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[UK]Partridge DSUE (8th edn) 1287/2: since ca. 1930.

2. (gambling) a horse or greyhound which is deliberately – for the sake of the odds – not meant to win, whatever legitimate gamblers may presume.

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[UK]D. Powis Signs of Crime 206: Undertaker’s job Specifically, a horse or greyhound not intended to win; generally, any hopeless proposition.
[Aus]G. Seal Lingo 142: An undertaker was a person who laid odds only against horses certain to lose, or dead ’uns. This evolved into the later term an undertaker’s job, meaning a horse that is not being run to win, that is, running dead.