(4 syl.). The Web or Shroud of Penelope. A work “never ending, still beginning;” never done, but ever in hand. Penelopë, according to Homer, was pestered by suitors while her husband, Ulysses, was absent at the siege of Troy. To relieve herself of their importunities, she promised to make a choice of one as soon as she had finished weaving a shroud for her father-in-law. Every night she unravelled what she had done in the day, and so deferred making any choice till Ulysses returned, when the suitors were sent to the right-about without ceremony.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Penelope from Fact Monster: