Ask HN: Networking and Under Performing Colleagues

I've seen some posts on Ask HN in general about the value of networking towards increasing your career prospects. While I do understand the value of not "burning bridges" in your company, how does on go about dealing with underperforming employees at work and networking with them outside of it?

Here are a few anecdotal cases from my work/team.

1. I have an underperforming colleague who just isn't interested in working and there's no easy way to let them go. There have been multiple instances in the past where I've complained about them to the manager for not pulling their weight.

2. There's an external vendor staff in our QA team and they're buddies with our manager and scrum leader. They don't pull their weight either and just send some emails on weekends and late nights, in what I assume is an attempt to show off that they've been working odd hours. The manager doesn't know the day to day working of the team and has delegated that to the scrum leader. This person sent me an invite on LinkedIn and called himself "test manager at ourompany", with no mention of their employer (the agency), in what I believe is an attempt at portraying to everyone that this person is actually full time at our company.

The work ethics of the two of them is questionable to me (different folks, different strokes). Should I still go ahead and network with them on LinkedIn for instance?

Have you been in a similar situation? What did you do?