I only ask this because of how fast light travels. The question remains in the title. Why, or why not, would this work?
I think the question is referring to situating a very large mirror in space facing earth. If we were to put it several light minutes away, then events occurring opposite the mirror could be reviewed de novo with more preparation upon the warning we received upon the first light of the event arriving at earth.
For example, a supernova going off in M31 might not be under observation at the moment its light first arrives, and so the initial observations might be lost. However, with a mirror facing M31, we would be able to observe that mirror as the event unfolded, having been warned that there was something worth watching, in advance.
Nice idea! But it would likely be much less expensive to simply have multiple telescopes always watching "prime" starscape for unexpected events.
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Yes, we always look into the past, when looking somewhere. There is for instance a mirror on the moon. When sending a laser beam to that mirror, we can detect the reflected light about 2.5 seconds later. This could be interpreted as looking 2.5 seconds into the past, when the laser has been fired. Details here.