Person A and Person B agree to share a piece of real estate
I assume this means that A and B jointly own the property. Correct? Did they memorialize their arrangement with a well-drafted contract? It doesn't sound like it, so I'll assume the answer is no.
Person B says "screw it" and stops paying their half of expenses which Person A is forced to assume.
What does "their half" mean? Person B is just one person, right? "Their" is a plural pronoun.
Over several years, Person A's extra expenses (paid on behalf of Person A) accumulate to exceed the cost basis of Person B's half of the property (with property value consistent to the sale price).
I think what you're saying is illustrated by the following example: A and B jointly purchased the property for $200,000, with each contributing $10,000 toward a down payment. Over the years, A's payment of 100% of "taxes, insurance, association fees and utilities" exceeds $20,000 such that the 50% that A paid that B should have paid exceeds the $10,000 that B contributed to the down payment. Is that what you're saying?
Person A, out of good faith, continued to pay 50% of rental proceeds to Person B the whole time.
That seems unwise and has nothing at all to do with "good faith."
Person B is demanding an immediate / on demand payout from Person A for 50% of the property value. Person A refuses, saying that the amount of payments which they assumed on Person B's behalf, now well exceed Person B's basis in the property (with no significant value appreciation). Does Person A owe person B anything?
Of course not. Unless there is a contract between A and B that entitles either of them to be bought out on demand, B isn't entitled to anything just because he/she makes a "demand." On the other hand, if A has the ability to buy out B, that might be an option worth considering.
A is certainly correct that his/her payment of expenses that B should have shared in entitle him/her to offset anything that would be paid to B (whether in a sale of the property or otherwise).
If I were A, I would consult with a local attorney ASAP and specifically discuss whether withholding any portion of future rental payments would be a good idea.