People can't always see the doors that are open in front of them. They may be focused on one thing or another that prevents them from seeing the potential that exists with a new connection or a chance encounter.
Very often, if that random event is not directly related to what someone is immediately doing, a person won't see the possibilities that exist and then ignore the opportunity. When I make a random connection, I at least stop to talk, DM, or email with the contact to see if there is any way to develop common ground.
Social media in particular has accelerated the rate at which people are connecting. With the right approach, one can make contact with luminaries in their field, with fans world wide, or with long lost friends. Social media also enables people to maintain relationships, however weak or strong, by providing a forum for people to interact. What you do with those connections is up to you.
When people approach me, I find that they are more often than not trying to sell me something. "Lets see if we have any synergy" is a phrase I hear frequently. The person usually wants me to check out their website and then see if there is some service that I can use. When I respond back to them that I like what they are doing and we should talk further about how we can develop common ground, the line goes cold. I guess they weren't interested in synergy.
For every twenty encounters like the one I just described, there might be one connection that develops further. But, you have to start the conversation first to see where it goes.
An alternate and more effective approach may be to give your best work away for free, share ideas and contacts, and make an effort to make useful connections for others. In doing so, you are creating value for others.
Lead with value and you may just find that doors of opportunity will open themselves.