Is "shifting definitions" a logical fallacy? Should it be?

This came up recently in a conversation on this platform. In consulting the dictionary definition of a particular term, it became clear that the term had both a denotative and connotative meaning, the latter of which changed the meaning in a significant way. Many words also have first, second and third definitions. Some even have first and second definitions that are antonyms!

There is a family of fallacies that covers this ground, including:

• the definist fallacy 
• the ambiguity fallacy 
• the appeal to definition 

But is there a general fallacy for when someone routinely shifts definitions to make invalid arguments seem valid? Should there be?

Example:

• Person A says "the 2020 election was literally stolen."
• Person B counters that if this were true, evidence would have emerged that voting machines were hacked, ballots had been forged, etc. No such evidence has emerged.
• Person A then makes various arguments about unfair media coverage, unfair advantages in early voting and mail-in voting, etc.
• Person B points out that this is a different argument since Person A said the election was literally stolen.
• Person A then argues that by literally he/she meant "figuratively."

Perhaps the above is a bad example since "literally" is one of those words where its second definition is its antonym. Making this argument, then, might fall under the appeal to definition. But I am asking a broader question since I see this sort of argument all the time. Indeed, debates often devolve into sub-debates about the proper meaning and understanding of words. Sometimes of a single word!

"It depends on what the meaning of the word 'is' is." - Bill Clinton

I do agree that this is common, but I tend to see this more on the side of rhetoric (hyperbole, exaggeration - which does have some fallacious overlap). I believe that being clear as possible and defining loaded language is the best strategy here. If there is any error in reasoning, it is in one making the assumption that they know what the other person means by the words they used.

Here is how I would respond to person A in your example:

Person A: the 2020 election was literally stolen.
Bo: What do you mean by "literally stolen?" Can you give an example of the most egregious example?
Person A: CNN called Trump a sociopath, so 8 million more people voted for Biden. Stolen!
Bo: "stolen." You keep using that word. I do not think you know what it means (said in my best Inigo Montoya accent). And stop getting your news from pillow salesmen.

Hedging.

The claim is substantially revised, then passed off as if it were similar.

"Literally stolen" =/= "figuratively stolen."

This does not seem to me to be a logical fallacy, but to the fickle rhetoric of one who participates in the debate.
The terms "literally" and "figuratively" are contradictory. Of course, the term "literally" is used because it is more dramatic and calls for greater condemnation. Imagine arguing like this:

Person 1: The sum of the interior angles in a square is equal to 180 degrees.

The opponent then constructs a square and, referring to its definition and the definition of the degree, proves that claim of person 1 is logically impossible.

Person 1: By square I meant triangle.

You see, it is impossible to identify a logical fallacy here because we need an argument for a logical fallacy, and here through speech that argument changes until it is obtained satisfactorily.