This is commonly denoted as optional:

available as a choice but not required

_{(source: Merriam-Webster)}

Another example:

The definition of a method, constructor, indexer, or delegate can specify that its parameters are required or that they are optional. Any call must provide arguments for all required parameters, but can omit arguments for optional parameters.

Something that is allowed to be missing is omissible. Wordreference.com defines omissible as:

capable of being or allowed to be omitted

https://www.wordreference.com/definition/omissible

In English grammar the object relative pronoun is omissible:

The book (that) I wanted to buy was sold-out.

The usual mathematical terms for these things (from the study of modal logic) are 'necessary' (for your 'guaranteed') and 'possible' (for your 'allowed'). All you need is negation to get all four possiblities.

• necessary - it must exist


• possible - it may exist


• not necessary - it may not exist


• not possible - it cannot exist

Depending on your (choice of) logic those two in the middle may be the same.

For a logic of probabilities, where 0 <= p <= 1:

• necessary: p=1


• possible: p > 0


• not necessary: p < 1


• not possible: p = 0

For example, you can see that 'not possible' is the same is the complement of 'possible'.

This mathematical use of these words follows our informal meaning.

So to your specific questions:

• 
  

  Which single word is able to replace the phrase "allowed to be missing?

  
  
  

  With respect to probability, this means that it could be any probability. So any combination that covers all possibilities, 'necessary or not necessary'

  
  


• 
  

  Which single word is the exact negation of "guaranteed to exist"?

  
  
  

  By negation, there are two possibilities that informal English allows. 1) the set complement, 2) the other point extreme of the spectrum.

  
  
  
  
  
  • For the set complement it is 'not necessary'.
  
  
  • for the other extreme it is 'not possible'.
  
  
  
  

This question is confusing as hell, but I think "unnecessary" or any of its synonyms might fit, depending on what you mean exactly, as I'm confused.

Something is allowed. (allowed to exist)
Something is
unnecessary (allowed to be missing)

You also have the condition:

Also, if I say that something is not ??? (allowed to be missing), then
it is guaranteed (guaranteed to exist).

If you place "unnecessary" or "unrequired" or "unneeded" where you placed the question marks, does that satisfy your needs? In other words, if something is not "unnecessary", or not "unrequired", or not "unneeded", does it make then make it guaranteed? I don't know.

dispensable

"More than you need and therefore not necessary; that can be got rid of."

Cambridge Dictionary

I would say RELEASED.

According to Macmillan Dictionary
https://www.macmillandictionary.com/dictionary/british/release_1?q=Release+#release_1__28:

RELEASE

FORMAL 

to allow someone not to have to do something

release someone from something: 

We were released from our classes in order to take part in the celebration.

I think the word you probably want is absent. If something is absent that means it is not here, and that can either be because it exists elsewhere, or because it does not have the existence necessary to be present anywhere, per the Century Dictionary and Cyclopedia's definitions:

1. Not in a certain place at a given time; not in consciousness or thought at a certain time; away: opposed to present.


2. Not existing; wanting; not forming a part or attribute of: as, among them refinement is absent; revenge is entirely absent from his mind.

Although it uses the nominal form of the word rather than the adjectival form, a phrase that very nicely demonstrates this is "The absence of evidence is not evidence of absence", which is a popular phrase in our current century according to Seth Augenstein, in the online Forensic Magazine article When is the Absence of Evidence Evidence of Absence?

The phrase itself is a good example because absence is used both ways. In the first case, we simply do not have the evidence to prove something exists at this point in time, yet that does not necessarily mean it is nowhere to be found as suggested by the second. It is a common rebuttal to the argumentum ad ignorantiam fallacy, particularly where somebody wishes to furnish the missing evidence. Consider this explanation excerpted from chapter 13 of Political Argumentation in the United States: Historical and Contemporary Studies. Selected Essays by David Zarefsky for instance:

Ordinarily the argument from ignorance is regarded as a fallacy in reasoning. It was first given the name argumentum ad ignorantiam by John Locke, and is one of the group of "ad-fallacies" that appeal to irrelevant considerations in order to warrant an inference. The fact that we do not know A to be true is no more reason to conclude that it is false than to regard it as true. The fallacy converts extistential doubt into a conclusive assertion of either truth or falsity.

The only problem with it, in my opinion, is that it is simply an adjective, rather than a past participle (in summary: a verb inflected in past tense form to be used as an adjective) so it would seem out of place among the other examples, but I think an actual adjective should suffice for all practical intents and purposes or at least for the table.

My initial thought was excused, just from reading the title alone. A person is excused if permitted to be absent.

However, I think exempt (or exempted) is a better fit. Wiktionary has a nice, concise definition:

Free from a duty or obligation.

In this case, free from the duty or obligation to exist.

Based on your table, it seems you have 2 booleans, existence and knowledge, giving 4 combinations. You want to name these 4 combinations, but this only makes sense from the perspective of a knowledgable 3rd party.

For example, if I had a ball and a screen and two people sitting on opposite sides of table. Person A either places the ball on the table or not and either places a screen in front of person B or not. From Person A's perspective:

Ball    Screen   Word(s)

YES     NO       Guaranteed / Exposed

NO      NO       Prohibited / Voided

YES     YES      Cloaked / Obscured

NO      YES      Evoked / Hinted

evoke: To cause the manifestation of something (emotion, picture, etc.) in someone's mind or imagination. [ https://en.wiktionary.org/wiki/evoke#English ]

I would use the word...omitted