I am partly responsible for every sin anybody has committed at least during my lifetime.
Here's why. I have sinfully acted in ways that made my prayers less deep, less frequent and less effective. But chief amongst the things I should be praying for is that God rescue me and my neighbor from sin. When my neighbor sins and I did not pray for my neighbor as I ought to have, I am partly responsible for my neighbor's sin—I have at least negligently failed to do something that, as far as I know, would have decreased the probability of my neighbor's sinning.
There are two general ways this has happened. First, there are the many cases where I directly failed to pray as deeply or frequently as I should have. Second, there are many cases where I sinned through something other than neglect of prayer. In the latter cases, I made myself more wicked through the sins, and hence made my prayers less effective—it is the prayer of the righteous that, it is promised, avails much—and made myself be less good at prayer. Besides, often, I could have spent in prayer the time during which I was sinning.
This is the communion of sinners. But we have a merciful God who became one of us and has made the communion of the saints possible.