Why was Abraham better able to protect Sarah from Abimelech as her brother than as her husband?

As recorded in Genesis 12 & 20: Abraham was afraid that Abimelech would kill him and take his Sarah from him if the king knew that they were married, so he said she was his *sister* instead. How did presenting her as his sibling rather than wife protect her from that? Couldn't the king still have killed him and taken her?