Participle clause is a flexible and versatile way to connect a subordinate clause with the main one providing concurrent information such as a reason or condition, parallel action or situation, or background information.
* The fruit was expensive, being imported = The fruit was expensive, because/as it was imported. (reason)
* The boys being chosen for the team are under 9. (this is a relative pronoun clause case)
Such use of "being" (present progressive tense) adds the sense of happening at the moment.
"chosen" in "the boys chosen ", only refers to the result of the action; it doesn't say when the choice was made at all.
"The boys being chosen" means the boys who are NOW being chosen, which is quite different.
Another example:
- He is funny => He has funny disposition and usually act or speak in a funny way.
- He is being funny => He may or may not be a funny person, but he is acting or speaking in a funny way right now.
* Having been hunted close to extinction, the rhino is once again common in this area.
The participial clause has essentially two tenses, simple ("being"), and perfect ("having been").
The simple tense indicates the same tense as the main clause, while the perfect means it is further past.
So compare:
1. Being hunted close to extinction, the rhino is ... => Even though it IS close to extinction, the rhino is ...
2. Having been hunted close to extinction, the rhino is ... => Even though it WAS close to extinction, the rhino is ...
In #1, the two clauses are in the same tense and therefore contradict each other (close to extinction <-> common).
#2 has a past-present arrangement. "WAS once close to extinction but is now common again", making clear sense.
Another example:
1. Losing my job, I have to watch what I spend => Since I lose my job, ... (unclear what it means - "lose" in the future?)
2. Having lost my job, I have to watch what I spend => Since I lost my job, ... (gives clear reason for the main clause).