Nothing changes at the time of "wave function collapse". When you measure one particle of an entangled pair, nothing actually happens to the other one. But you don't need to listen to me, check this out:
The wave function collapse and "spooky action at distance" for entangled particles are somewhat different concepts. The collapse idea arises as a part of Copenhagen interpretation, which states that particle always exists in a superposition state (aka wave function of probabilities). So when audience asks, "well why is it that my measurement device showing particle exists/doesn't exist in one place"? The interpretation then says, "That, my dear fried, is because the wave function collapsed to a single state just when you did the measurement". People have been trying to explain and figure out what/why/when this collapse occurs to make sense of Copenhagen interpretation.
That's true, but such proposed extensions or alternate interpretations are then filling in the gaps that would lead people down the path of the simulated universe in the first place.