Let's visualize the question. The universe is a space, where our physical universe is a plane moving through space. 2 spatial dimensions, and the 3rd one is time. Maybe human consciousness moves through the space, maybe it just observes single plane at the time, who knows.

What happens after the plane reaches the end of that space?

I don't know where I'm getting at. Maybe I'll write another answer later.

First option is that only a single plane exists at any given moment. This'd make it trivial to say where the plane would be, had the whole space not stopped existing.

Second option is that all the planes exist simultaneously, and there are no moments after the space's end. That means there is no moment after the time has ended where to ask how long has it been since the world and time ended. If something was to exist, which would be impossible, it could still refer to the time when some moment existed.

Third option is that the whole space stops existing after some amount of time - and the time represents the 4th+ dimension of our universe. No idea how this would work.

The second option I believe is what the current physics claim to be correct, but as I believe that human consciousness moves through time, the time could be measured according to the first option based on where consciousness would be.

How do we know that there was no "time" before the Big Bang? Modern scientists are talking about what happened before the Big Bang, and how the Big Bang occurred. If anything happens before or after the Big Bang, "time" continues to exist, as "time" is simply relative change.

Seconding Harry Hindu, with this addition. Time is not always well-defined. Where (when?) it is not well-defined, it cannot be accurate to say that there is no time. Even with simple relativity it gets weird. Imagine a clock on a moving spacecraft: it measures the passage of time. How about the passage of time in the space the spacecraft is passing through - that's a different time. Same space, different times, apparently without limit. I think you don't really get to know this stuff; you just get used to it. Corrections accepted.

Suppose the universe died. The theory of the Great Crunch has come true. We have a state what was before Big Bang. There is no time. It is in such a case we can talk about that "someday" or "sometime" universe existed? There is no time but we know that the universe existed. Now it does not exist, and time does not exist. So you can say that the universe existed after it "died"? — carl37

Your thought experiment is impossible, contradictory nonsense. You project yourself to a fictitious future time, a time in which the universe does not exist any more, and then you propose to be saying, at this time, "the universe existed". But it is impossible for you to be at this time, when the universe does not exist anymore, so it is impossible for you to be saying, at this time, "the universe existed". Therefore your statement "there is no time but we know that the universe existed" is pure nonsense because there would be no "we", and so nothing that "we know", if the universe ceased to exist.

It's always interesting to test the limits of the human mind. I'm no genius so I may not say anything worthwhile.

Anyway...

One way to make sense of it is to bisect the meaning of "after" as follows:

1. Temporal after as in what we mean when we say ''come after 2 o'clock''

2. Non-temporal after as in what we mean when we say ''the glass broke after a stone hit it''

Meaning 1 of "after" wouldn't make sense since with the destruction of the universe time would lose meaning.

Only meaning 2 of "after" makes sense as simply one event following another.

Am I making sense?

In my view everything exists timelessly, as logical necessities. But among these things are certain arrangements/orders that we experience as temporal sequences. These arrangements must satisfy certain conditions, for example (but perhaps not necessarily) theory of relativity.

is pure nonsense because there would be no "we", and so nothing that "we know", — Metaphysician Undercover

I rather thought "we" were "timeless observers".
I meant something like a line. At the end of this line ends the Universe. But this line "existed". In any space and in any time. So "we" as a timeless observer we can say that Universe "existed", when there is no time?

It is in such a case we can talk about that "someday" or "sometime" universe existed? — carl37

You seem to be asking if we can talk, at the point where the universe no longer exists, about the universe--that is, as if we could be at the point where the universe no longer exists. That's further evidenced by you saying, "There is no time but we know that the universe existed"--as if we could somehow literally know that where it's in the past tense instead of just imagining it. But obviously we couldn't be at that point, as we wouldn't exist either if the universe doesn't exist.

When we're talking about something, we're doing it at a point where the universe exists, where we have a temporal and spatial location so to speak.

So you can say that the universe existed after it "died"? — carl37

If it doesn't exist, you're not going to say it exists.

Yes, that's exactly what I said is a nonsense contradiction, that "we" refers to timeless observers.

So I'll take it differently. Is it possible to say that the universe "existed" in the past when there is no time? Is it time that is unnecessary here, because it is that our universe has come into existence and time has no effect on it, because it is a fact, it existed, regardless of whether the time is over? It had its own space and time, so it can not be said that despite its remains it existed? Since it exists despite the fact that it "died" and there is no time it can not be said that it did not exist?

To answer your question, once must first dispose of scientific time which is merely synchronizing movements of physical clocks for measurement purposes, and inspect time for what it actually is, as we experience it in our lives. Time is psychological and is a manifestation of our mind (not to be confused with the brain) as it compares memories slowly morphing from one state to another and prepares for possible actions in the future.

If one fully introspects time for what it is, one can view time as entangled with consciousness (memories). Without this there is simply quantum stuff out there that is changing wave form but absolutely no sense of time. It has no beginning, had no end, and cannot be destroyed. As an addendum, conscious itself cannot be destroyed as it is embued into these wave forms.

Is it possible to say that the universe "existed" in the past when there is no time? — carl37

No, I think this is impossible. The concept of "past" is dependent on the concept of "time", such that past implies time. So past, as something real which we could refer to, is only possible if there is time. Consider the concepts of "human being" and "animal". To ask if there could be a past without time is like asking if there could be a human being when there is no animals.