Of course they did, and so did everything. Feeling suicidal tends to make you look away from the consequences and all things that matter tend to be pushed aside. It's a feeling of desperation, desperation to break away. Whatever the catalyst it feels inescapable and you begin to doubt everything, how you are perceived or the impact you've had. You're forced to put on a brave face or people will begin to question, point fingers and try to help but if anything it doesn't at all: it makes it worse. It takes a lot to confront your fears but when you're depressed you see no other way out, no other option to make things better. Whether or not Chris Cornell's suicide was the catalyst in Chester's suicide is up for debate but whatever the cause it was enough to push him over the edge.