I would have no theoretical (as opposed to practical) problem with this sentence

The woman [that] the man [that] the girl loved had met [last week] died [earlier today].

But to me a crucial break in coherence occurs in the sentence

The woman the man the girl loved met died.

because here the author tries to make met stand in for had met, forcing readers to make sense of past actions that clearly have different moments of occurrence and durations, without providing cues that the sentence's author could have used to clarify the sequence of actions described. Notably, the man presumably met the woman before the woman died, so the author really has no excuse to obfuscate that point by rendering both the meeting and the dying in simple past.

Switching now to the all-simple-present iteration of the sentence—

Women men girls love meet die.

—we have to accommodate the oddly definitional sense of the sentence, to grasp its meaning:

Women [that] men [that] girls love [happen to] meet [must] die.

If you were actually trying to convey the sense of that sentence intelligibly, I think you would probably frame it in terms less like the original and more like this:

Women who meet men that girls love are sure to die.

(As, of course, is everyone else.)

I hesitated to answer this question because I'm not much interested in it as an exercise in structural logic. But it seems to me that the only grounds on which one can claim that "Women men girls love meet die" is "a valid sentence" is by quarantining validity a considerable distance away from any commonsense approach to sentence construction and interpretation that would normally guide a speaker seeking to be understood and a listener trying to understand.

It may be that a heavily armed analyst can justify a bad sentence like the OP's under some strained or mechanistic parsing of its components; but in my view (and invoking the traditional wisdom of Flannery O'Connor), a speaker with a good sentence don't need to be justified.

I would have no theoretical (as opposed to practical) problem with this sentence:

The woman [that] the man [that] the girl loved had met [last week] died [earlier today].

But to me a crucial break in coherence occurs in the sentence

The woman the man the girl loved met died.

because here the author tries to make met stand in for had met, forcing readers to make sense of past actions that clearly have different moments of occurrence and durations, without providing cues that the sentence's author could have used to clarify the sequence of actions described. Notably, the man presumably met the woman before the woman died, so the author really has no excuse to obfuscate that point by rendering both the meeting and the dying in simple past.

Switching now to the all-simple-present iteration of the sentence—

Women men girls love meet die.

—we have to accommodate the oddly definitional sense of the sentence, to grasp its meaning:

Women [that] men [that] girls love [happen to] meet [must] die.

If you were actually trying to convey the sense of that sentence intelligibly, I think you would probably frame it in terms less like the original and more like this:

Women who meet men that girls love are sure to die.

(As, of course, is everyone else.)

I hesitated to answer this question because I'm not much interested in it as an exercise in structural logic. But it seems to me that the only grounds on which one can claim that "Women men girls love meet die" is "a valid sentence" is by quarantining validity a considerable distance away from any commonsense approach to sentence construction and interpretation that would normally guide a speaker seeking to be understood and a listener trying to understand.

It may be that a heavily armed analyst can justify a bad sentence like the OP's under some strained or mechanistic parsing of its components; but in my view (and invoking the traditional wisdom of Flannery O'Connor), a speaker with a good sentence don't need to be justified.