How would you call the action of discovering things about someone's past?
For example, finding information of someone and you came across with stuff you didn't want to find.
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There's an idiom that might fit here: skeleton(s) in the closet.
Wikipedia describes this as:
a colloquial phrase and idiom used to describe an undisclosed fact about someone which, if revealed, would have a negative impact on perceptions of the person
So, you could use the phrase like this:
I'm starting to regret thumbing through my wife's old address book – too many skeletons in the closet.
It wouldn't be universally applicable to the situation you describe:
Finding information of someone and you came across with stuff you didn't want to find.
For example, if you found out that your best friend was recently diagnosed with cancer, that wouldn't be a cause of embarrassment or shame, so it wouldn't be regarded as a “skeleton in the closet.”
The Phrase Finder defeins this expression as:
A secret source of shame ... which a person or family makes efforts to conceal.
While the Idiom Reference website says:
Embarrassing or incriminating secrets from your past.
How about this:
surprising or shocking revelations about one's past
The other day I was rummaging through some old things of my father's when I stumbled upon a bunch of really old photos and it was quite a shocking revelation for me to learn that he had dozens of female lovers when he was young. Who could've thought that my father was a ladies' man? He certainly doesn't look like one to me now.
You appear to be asking for a verb, i.e. a name for the action. In order to choose, one needs to know whether the discovery was accidental or not.
If accidental, you might say "stumble(d) on" (accidental and surprising), or perhaps "came across" (accidental but less shocking).
If the find was on purpose, you might say "uncover" or perhaps "investigation revealed".
To put it together with J.R.'s nouns:
I stumbled on a skeleton in her closet
Investigation revealed several skeletons in his closet
I uncovered shocking revelations about X's past