Halliday & Matthiessen (2014: 469):
When the non-defining clause is an ‘intensive’ relational one, the Process may be left implicit; for example:||| DPP lawmaker Chen Ting-nan will be the justice minister, || responsible for helping Chen keep his promise to clean up graft. |||where responsible for ... is Attribute; compare the non-finite version with the Process: [Process:] being [Attribute:] responsible for ...
As is usual with non-finite clauses, the meaning is less specific; both in the domain of the dependent clause and its semantic relationship to its domain are left relatively inexplicit. There is no WH- form, as there is with finites (in this respect non-finite non-defining relative clauses differ from defining ones); nor is there usually any preposition acting conjunctively, as there typically is with non-finite clauses of extension and enhancement such as besides or on in besides selling office equipment, on leaving the building.