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If your opponent takes control of your "Malice Doll of Demise", and sends it to the Graveyard by the effect of a Continuous Spell Card, you can still activate its effect to Special Summon it during your Standby Phase.
If "Malice Doll of Demise" is Tributed to activate the effect of "Mass Driver", then "Malice Doll of Demise's" effect does not activate because the Tribute is treated as a cost, not an effect.
If "Malice Doll of Demise" is Tributed to activate the effect of "Mass Driver", then the effect of "Malice Doll of Demise" does not activate because the Tribute is treated as a cost, not an effect.
Examples of Continuous Spell Cards that would send "Malice Doll of Demise" from the field to the Graveyard by their effect include "Ectoplasmer" and "Continuous Destruction Punch".
You can only activate the Special Summoning effect of "Malice Doll of Demise" during your first Standby Phase after it was sent to the Graveyard by the effect of a Continuous Spell Card. If you miss that, you cannot then activate the Special Summoning effect later on. If there is no monster card zone at the appropriate time, the effect is activated but you cannot Special Summon the "Malice Doll of Demise", so its effect disappears.
The effect of "Malice Doll of Demise" activates in the Graveyard. If "The End of Anubis" is on the field during the Standby Phase in which "Malice Doll of Demise" would activate its effect, then the effect is negated and "Malice Doll of Demise" is not Special Summoned. If "The End of Anubis" leaves play after that, you still cannot activate "Malice Doll of Demise"'s effect because the opportunity has passed.
The effect of "Malice Doll of Demise" activates in the GY. If "The End of Anubis" is on the field during the Standby Phase in which "Malice Doll of Demise" would activate its effect, then the effect is negated and "Malice Doll of Demise" is not Special Summoned. If "The End of Anubis" leaves play after that, you still cannot activate the effect of "Malice Doll of Demise" because the opportunity has passed.