Circuit with a threshold
One possible option here is a Zener diode, which is a type of a diode with a well controlled breakdown voltage achieved by a particular doping profile.

When a Zener is reverse biased, the current is very low until the reverse voltage gets to a specific level, after which the current sharply increases.

This sharp current increase is similar to that of a regular forward biased diode, but you have flexibility of choosing threthold voltage level.