The one with "the" would be all right in certain very specific contexts, for example:
I was searching around in an attic and came across an old trunk of my grandfather's. It was securely locked and I with great difficulty opened it. No wonder it was locked. Inside I found documents that showed he came into this country illegally, that he was imprisoned in his native land, and that he h
No, that won`t work, Summit. 'Pandora's' remains a possessive there, which cannot co-exist with 'the' determiner. 'It was like opening Pandora's box / a Pandora's box.
There's no problem grammatically with using "the" with a possessive, as in "I opened the captain's trunk." The "the" in the example is okay because it is "the" trunk, which is like "the" box.
I'd like to look back at Anon (Summit's) earlier post presenting a use with 'the', because it finally dawned on me what he was getting at: I agree that under limited conditions 'the' is possible when speaker or listener already realizes the metaphor. I'd like to re-work Summit's example to make this clearer:
I was searching around in an attic and came across a mysterious old trunk of