What is the difference between this "the day" and "per day" before?
It happened per day before this(something).
It happened the day before this(something).
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Sign up to join this community"Per" and "The" are very different words. As a result, your first example makes no sense at all, to the extent that I cannot offer an alternative!
Your second example is better; without knowing the full context, I would probably alter it to: "(Something) happened the day before this."