I'd say The Messenger is a good example of this.

Bloodborne (more on the meta side), Dragon Quest XI, NEO: The World Ends With You, The Sexy Brutale, Ghost Trick.

@DeltaWDunn
True I forgot about that, I'll add it good suggestion

@AlphaOne2
I'll look into those, Ghost trick definitely fits and Neo

Bastion probably fits here

Nice list! The original Final Fantasy is like this, but in reverse from what you're saying I think? In it, the big bad is the one initiating the time loop and the heroes save the day by breaking it.

this thing is gonna fill up with VNs if you're not careful

Outer Wilds

@Funbil Oh, you're right. Yeah a lot of VNs do that I wasn't thinking about that genre

@cowboyjosh
That's true, I think some of the crystal chronicle games and FF5 also kind of did that

@ChillyRama
added it, good suggestion

Deathloop?

@TimAlien
I'll add it