This week, a kind of sad theme emerged. I talked to a string of people who were mid-way through very successful careers.
They had started with a major, name brand companies right out of school. They had worked hard and been promoted to some pretty senior roles. It was clear looking at their resumes that they had gone above and beyond for their companies and their careers had flourished.
Until the day that they got outsized, right sized or downsized and realized that their entire network of references and connections were contained within that single company.
Most were part of large groups that got laid off at the same time so while those “layoff buddies” were good for commiserating and going to outplacement sessions, they were not good for leads to new roles because they were looking too.
Don’t let this happen to you.
LinkedIn is the best thing going to prevent this from happening. When you meet someone at a conference, connect. When you are on a panel with someone, connect. When you meet someone interesting at a cocktail party, connect.
Go one step further. When someone leaves your company and gets another job, send a note. LinkedIn will tell you when this happens. Use this information to continue building your network so that it extends past your silo.
You may never need to lean on your network for career help, but it’s nice to know it’s there if you do.
Recruiter's Couch 
I have seen this happen too. You offer some excellent advice! People often don’t realize how narrow their network is until something like a layoff happens.
Knowing people outside of my former place of employment is what got me a new job when they ***sized me.