When you have a word which, when pronounced one way, has one meaning, but pronounced in a different way, has the opposite meaning.
So for example; resign (to quit) and resign (to join up again).
A contronym (provided the pronunciation is not required to be different).
Here’s a whole bunch.
Also note that your second word would typically be presented as “re-sign”.
Antonymic Homophone?
I don’t think the OP is talking about contronyms. (Same word, opposite meaning)
The way I read it is…same word, but the pronounciation and/or context give it a different meaning, but those meanings will not necesarily be contradictory.
Live:
“Live bait” or “why don’t you live a little”
Contract:
“I may contract herpes if I sleep with you” or “I don’t feel comfortable signing that contract”
Right:
“I have a right to live” or “Take a right at the next stop sign.”
OP is just pointing out why the English language is difficult to learn.
Actually, I was. 
And thanks for the answers.
One must wonder why this particular sentance popped into your head
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Colibri
General Questions Moderator
There is also the concept of words pronounced differently but spelled the same. I once got a list of over 100 of them. I called them heterophonic homographs, but homographic heterophones would work just as well.
I’d call these homographic heterophonic antonyms, or maybe heterophonic contronyms.
You realize that this is basically practically every single word in the dictionary? There is hardly any word which means just one thing.
Also called Janus words or autoantonyms. Here’s even more of them.
This topic comes up all the time in SD. Lotta people like words here.
[nitpick]“Contranyms.”
The funhouse of polysemy is large. The “See also” of the Wiki entry leads to more analyses of these twisted mirrors in language (their optics, to belabor the metaphor).
If it’s not in Silva Rhetoricae, it ain’t anywhere, I’m guessing.
My favorite word that has a (slightly) different meaning when pronounced differently is “arithmetic”, probably because most people don’t even know the other pronunciation or what the hell it means. (Stress on the third syllable; it becomes an adjective) I wouldn’t know of any words that change in pronunciation in order to express the exact opposite meaning like can be done with the word “cleave”.
Perhaps I shall take it up as a project to find one. I project it will take a long time to find one.
Actually many other languages have a greater frequency of homonyms than English.
So we can call it a reason languages are difficult to learn, and prone to misunderstandings.
I’m entranced. Where do I get in?
Ha!