The Precursors are connected to time and space; hence why they could be killed by the Forerunners and then be turned into the Flood.
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The precursors take various forms throughout the cosmos and create various forms of life, in the case of the forerunners the chose to allow them to kill them because they had never been wiped out before and they thought be interesting. However this does not affect their conscience as they are beyond time and space they can exist within reality but they're not bound to it. The flood were create when precursors reduced their forms to dust to be revived at a later date (they had sentimental value of their forms) but got corrupted after 10 million years (possibly primordial shenanigans) and were consumed by animals.