Are there known paradoxes regarding a detector that was, before use, entangled with a particle it detects?

Is it possible to design a system where a detector is entangled with the particle state it detects (before it is detected), and to create a paradox from this?

Upon observance of a state by the detector, a correlation between the particle and any entangled particles will instantly occur; fi a reverse spin. What if these happen in the detector and affect detection?

I cannot think of any paradoxes or “deadlock” scenarios but I was wondering if literature knows of any.

I think it could be somewhat of an argument against traditional simulation theories.