Another Chance was Determination's original Rare Spell Card, alongside Same Fate. Previous Versions can be found here.
Current Order: Toriel -> Alphys -> Undyne -> Sans -> Papyrus -> Asgore.
Since Beta 52.1, Another Chance functions very similar to the removed Sacrifice. For 2G, it can kill an ally monster of your choice. When doing so, you will restore 3 HP and the next Lost Soul in line will be summoned.
Check the Lost Soul image for the order they are given. It matches with DT's Passive as well as Resurrection and Will to Fight. Universal among all 'Lost Soul Generators', Thrashing Machine cannot be obtained. If any of the 3 spells is used by a non-DT player and they obtain a Lost Soul, it will instead be a random one.