Hardly an encounter, more like bumping into someone! An encounter possibly suggests a bit of planning and expectation of something happening. Bumping into is an accident.
The first thing to say is that there is no blueprint for an encounter. Only a few principles to follow in the interests of the parties involved, usually just two.
Every day we bump into people we do not know. Some, of course we will.
Dealing with the unknown means that when we cross paths with someone we do not know it might become an encounter. Something happens that causes the Connector to think it might become an encounter. Something triggers. But what is triggered needs to be matched by a response on the part of the other party. It is two sided and control of the encounter must remain with the other person.
Remember that a Connector is NOT a solution provider. They are a signpost to possible help. The signpost might be a very small first step. A Connector will likely not know what happens next.
How does a conversation start? Take a look at the framework below. It is not a formula!!!!
Open small talk which may become something that both parties pursue
To the right there may be some ideas shared for a first/next step. Anything that is related to health (physical, mental, spiritual should be signposted to specialist services. Attending a Talking Place for a second consideration of need(s) may be appropriate.
Just talking through issues can be freeing particularly for a person who is isolated or lonely. A problem shared is a problem halved.
It is very important to give people time to talk. If a Connector is already busy on doing something everyday (like picking up children from school) then they will likely not be looking to engage!
Common sense really.