What is your responsibility as an individual when viewing a webcast if you witness a suicide or read a post of someone talking about suicide?
It's a little unclear from your question if you mean legal or social responsibility, or if this is in a professional setting or not. In any case, the humane, conscientious, moral and ethical thing to do in such a situation is to try and intervene to get the person help as quickly as possible. Both a webcast and an online post of someone threatening or attempting suicide is a public cry for help. The person is suffering from mental illness, emotional issues or depression, and wants someone to intervene, hence the public display and appeal.
Time is of the essence in these situations. A direct post/comment, etc. to discourage the person from hurting themselves is the most important. They need to see that someone does not want them to do this, even if it is a stranger. As you are doing that, it is a moral imperative that you contact the authorities, dial 911, even if the webcast is in a different locale or the person lives in another city (which is likely) it starts law enforcement intervention and they can begin to track where the person is posting from.
Consider what you would feel like if you did nothing? While the law cannot prosecute you in most cases for failing to act, such inaction could haunt a person for the rest of their lives in terms of their conscience and self worth.