As a spell or ability an opponent controls resolves, if it would force you to sacrifice a permanent, you just don't. That part of the effect does nothing. If that spell or ability gives you the option to sacrifice a permanent (as Desecration Demon does), you can't take that option.

Sigarda's ability affects only sacrifices. It won't stop a creature from dying due to lethal damage or having 0 toughness, and it won't stop a permanent from being put into its owner's graveyard due to the "legend rule." None of these are sacrifices; they're the result of game rules.

If a spell or ability an opponent controls states that something happens unless you sacrifice a permanent (as Mogis, God of Slaughter does), you can't choose to sacrifice a permanent. On the other hand, if a spell or ability an opponent controls instructs you to sacrifice a permanent unless you perform an action (as Killing Wave does), you can choose whether or not to perform the action. If you don't perform the action, nothing happens, since you can't sacrifice any permanents.