Final answer:
The statement is false; a hyphen is not used after a noun when 'well' and a participle are part of a verb phrase or modifier following the noun, as hyphens primarily connect modifiers before a noun.
Step-by-step explanation:
The statement "Well and participle after a noun, the hyphen is dropped because the participle becomes part of the verb phrase." is false. The hyphen is used to join words serving as a single modifier before a noun. When the participle comes after the noun and is part of a verb phrase, whether a hyphen is used does not depend on the participle's position but on how the words function together. A participial phrase that comes after a noun doesn't require a hyphen since it's modifying the noun and not acting as a single modifier before the noun. For example, in the sentence 'She entered the room, looking radiant'. Here, 'looking radiant' is a participial phrase modifying 'she'. Since it comes after the noun, no hyphen is needed.
However, when multiple words before a noun serve as a single modifier, they are often connected with a hyphen to avoid confusion. For instance, 'She is a well-known author', here 'well-known' is a compound modifier that comes before a noun and requires a hyphen.
When the words 'well' and the participle come after a noun, they are typically not hyphenated, regardless of whether the participle is part of the verb phrase or not, because the standard function of the hyphen is to clarify compound modifiers that come before the noun they modify.