I am impressed by Loob's hypothesis (post #47) that two forms of reduction were being confused. I'm sorry that the text had to be removed, because it might have shown whether this is correct. However, I did find a webpage that discusses the substitution of a participial phrase as a type of reduction of relative clauses:
2. Clauses reduced to phrases:
Clauses (restrictive or nonrestrictive) in which who, which, or that is the SUBJECT can be reduced to phrases by omitting the relative pronoun and the part of the verb that agrees with the subject:
SOURCEClauses (restrictive or nonrestrictive) in which who, which, or that is the SUBJECT can be reduced to phrases by omitting the relative pronoun and the part of the verb that agrees with the subject:
[It lists several options. I include only the relevant rule.]
b. if the verb phrase does not begin with be , change the verb to the present participle (-ing) and omit the relative pronoun.