There are a few different processes followed, depending on how significant the overdraft is. One of our more common scenarios is improper authorizations leading to OD. I assume most are familiar, but for the sake of clarity... We're talking about things like Hertz getting an auth for $200 (which is approved because the balance is $250), and then the customer crashes the car, so Hertz decides to clear the auth for $2,000, resulting in the account balance going to -$1,750. In that case, we wouldn't even contact the CH. We would just process an authorization chargeback for $1,800.
In instances where the CH authorized the charges the caused the OD, there's minimal collection efforts made until it has been 30 or 60 days (depending on amount).
Last is something like a bust-out, where it appears the customer has done it intentionally (such as a bad deposit to inflate the balance). Those are handled by a separate fraud team, and I'm not familiar with what all their process entails.