Not allowed by my parents, I couldn't go to the party.
Does this participle construction grammatically work?
No, completely unnatural.
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anonymousDoes this participle construction grammatically work?
No, that sentence is not good. The two parts of your sentence say the same thing. Generally speaking, the second part of the sentence would say what you did instead.
You can use that construction, however:
Not allowed their own clothes, they wrapped themselves in bedsheets.