Facebook Inc. shares sank 6.3% to a record low on Thursday, falling below $20 a share on a day when some early investors were allowed to unload their stakes, adding further pressure on the beaten-down stock.

Rules expired Thursday that had restricted some early investors from selling down their stakes after Facebook's initial public offering. More than 271 million Facebook shares became eligible for sale Thursday, though holders could also choose to keep some, or all, of their stakes. Any additional shares would add to the...