I have read a rule of relative clause reductions, and it states,
2. We can use participles when reducing the sentence.
a) Present Participle "V-ing" (simultaneous)
1) We stood on the bridge which connects the two halves of the city.
//the relative clause is a defining clause.a) We stood on the bridge connecting the two halves of the city.
//omitting by replacing them with present participle
Since the example has stated only about a sentence that contains a defining clause, that makes me curious whether we can also omit the pronouns with or without the to be verb in the non-defining relative clauses of the sentences below,
2) Clare, who works with me, is organising the London marathon this year.
3) Clare, who is working with me, is organising the London marathon this year.
into this sentence:
b) Clare, working with me, is organising the London marathon this year.
If so, why?