The parents urgently seeking child care could put their immediate efforts into convincing a friend or family member to help out for a week or two, [buying] [them] time to look for permanent help.
What is a subject of "buying"? Is it parents? Then, I think, "them" should be "themselves".
Please help me
As a participle it doesn't have a true grammatical subject, but I would say that the logical subject is implied to be something like "getting a friend or family member to help out for a week or two".
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As a participle it doesn't have a true grammatical subject, but I would say that the logical subject is implied to be something like "getting a friend or family member to help out for a week or two".