fused participle
Definition - A participle regarded as being joined grammatically with a preceding noun or pronoun.

Note: Some consider this a usage error. They feel that the preceding noun or pronoun should use the possessive apostrophe or the possessive case to distinguish it from the participial phrase that follows.

Example -
I objected to him drinking so much. (fused)

I objected to his drinking so much. (unfused)

Oxford English Dictionary -
The term's first citation is from 1906:
"The mistake is caused by certain types of sentence in which a real, not a fused participle is so used that the noun and its (unfused) participle give a sense hardly distinguishable from a possessive noun and a gerund."
(H. W. & F. G. Fowler King's Eng. ii. 119)

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