Lead score is negative for many people who have opened/clicked our emails

They must have qualified for a smart campaign that deducted points from their score for some reason. Open one of the leads and go to activity history. You will see when the lead's score was lowered and the smart campaign that did the lowering. Then, check the qualification rules for that smart campaign.

Negative scoring is a tricky topic, especially if you have them on delays, or non activity - the negative score can compound quickly and you can have someone take a positive, MQL type activity, but due to the engative scoring still not trigger.

If you are using negative scoring, consider some campaigns that can neutralize the negative score from time to time if they are still fresh.

You may also consider doing custom scoring fields for negative scoring based up campaign streams so you are up and down within a stream not entire score.