The real problem was not a failed element (though it had been replaced twice previously) but a dirty and corroded spade connector. Since the electrical contact was not clean, it had obviously been arcing and the metal contact eventually burned and part of the now-blackened connector literally broke off. When replacing an element, the lesson here is to check that the spade terminals (that connect to it) are also clean, shiny and tight-fitting - and if not, replace them - but be sure to buy the correctly-rated spade terminals from an appliance store and use a proper crimping tool to connect them (the regular, big hardware stores seem to sell neither oven-rated spade terminals nor decent crimping tools).