Mixing Tenses and Times
The whole four-dimensional universe, including past, present and future times, does not change; it will not be different tomorrow; it remains the same at all times.
If the whole four-dimensional universe remains the same at all times, then presumably no part of it will ever fail to exist or has ever failed to exist.
So for example, the apple I'm just about to eat will never fail to exist. It will exist forevermore. As will I, and you, and this weblog.
In general, nothing that exists now will ever fail to exist.
What's going on here, and here, is (I believe, more or less like Irem and Rich) that when we use tense or modal operators, we usually restrict our quantifiers to the things existing at a particular time or world. Which makes pragmatic sense because otherwise the tense or modal operators are mostly redundant: if "there is" ranges over all possibilia, then "it is possible that there is" is equivalent to "there is"; if "there is" ranges over all (things at all) times, "it is, was or will be the case that there is" is equivalent to "there is".
This is why confusion arises when one begins to mix talk about other times/worlds with tense/modal operators. If "exist" in "no actually existing thing is such that it is possible that it does not exist" is the possibilist quantifier, then the sentence is true, and equivalent to "no actually existing thing does not exist" (again with possibilist "exist"). But it is very hard to read "exist" here as a possibilist quantifier, accompanied as it is by so many boxes and diamonds.
"This is why confusion arises when one begins to mix talk about other times/worlds with tense/modal operators."
I agree. I think that the so-called McTaggart's Paradox (the part of his argument which is supposed to show that nothings can be either past, present, or future) is also a result of that type of confusion.