I think you are offering up a false alternative.

It really is a choice between three outcomes. (1) No factory is built, no taxes collected. (2) Factory is built, company pays full sticker price on the taxes. (1) is unappealing because nothing is created. So we arrive at (3), where the company understandably wants to renegotiate the sticker price on the taxes and the taxing body doesn't want to end up in scenario (1), so they come to an agreement somewhere in the middle.

Why is this translated into the company received cash from the taxing entity?

Is there a way to find out how much Foxconn pays in U.S. taxes right now? Or how much revenue they earn in the U.S.? If Apple has Foxconn make phones in Taiwan, and Apple then ships phones to the U.S., then Foxconn doesn't pay any taxes to the U.S. on those transactions, right? Only Apple would right? If Foxconn doesn't pay any tax to the U.S. right now (???), and they build a factory in the U.S. and don't pay any taxes in the future, then it is a wash (except for now the U.S. employees would be paying income tax, etc.). Or am I missing a piece of the puzzle? (As in, maybe Foxconn is currently paying a lot in U.S. taxes from whatever operations they have in the U.S. currently?)

Let's say you want to take a portion of my income in exchange for career services that has a cost of 1,000 dollars a year for you to provide.

You say "pay me 20% of your 100k job" netting you 19k, I refuse to pay that steep of a fee and counter with "take 10% or nothing" netting you 9k.

I don't believe its fair to say that you have lost 10k if you accept my terms as the alternative is receive nothing. You have increased your revenue by 9 thousand dollars as opposed to earning 0 dollars. The option you proposed is simply not on the table and can't really be considered.

Those taxes are a cost of doing business in the state - akin to the rent on a property. If nobody wants to rent your property at your asking price, you can let it sit empty and get zero, or lower your price and get more than zero. You are not "forgoing" anything by lowering your price in that case. You never had that revenue to give up in the first place.