Often this represents the defensive shell you might use to avoid hurt or sexual or emotional involvement. The soft centre either being your vulnerable feelings or ego, or the female sexual organs.
Through common association of eating oysters as an aphrodisiac the oyster can also figure in dreams in which you are looking at your sexual energy or fears.
The oyster can also indicate being tight lipped, secretive or frigid.
If the oyster lacks a shell it shows your naked vulnerability, or naked sexual feelings. See: Pearl.