Why would you choose to be an American taxpayer without getting any of the benefits of citizenship or residence?

The situation, in a nutshell: you and your spouse are both U.S. citizens. You renounce your citizenship, but your spouse remains a U.S. citizen. You can elect (discussion below) to be treated as a U.S. taxpayer, even though you are no longer a U.S. citizen and are not living in the United States.
What the election does :
If you elect to be a U.S. taxpayer, the result is that you treated like a resident for income tax purposes, and for withholding on wages paid to you:
A nonresident alien individual with respect to whom this subsection is in effect for the taxable year shall be treated as a resident of the United States—
(A) for purposes of chapter 1 for all of such taxable year, and (B) for purposes of chapter 24 (relating to wage withholding) for payments of wages made during such taxable year.

See 26 U.S.C. §6013(g)(1).

1. Makes you taxable on worldwide income

"Chapter 1" means Title 26, Subtitle A, Chapter 1 of the United States Code. It contains Sections 1 - 1400UU of the Internal Revenue Code. These are the rules that impose income tax.

This means that a nonresident alien (you, the recently renounced citizen, now a nonresident alien) is subject to U.S. income tax on worldwide income.

2. Withholding on your wages

"Chapter 24" refers to Title 26, Subtitle C, Chapter 24 of the United States Code. It contains Sections 3401 - 3406 of the Internal Revenue Code. These are the rules that say an employer is supposed to withhold tax from wages paid to you, and remit the withheld tax to the IRS.

This means that if you have "wages" as defined in Chapter 24, your employer will withhold tax on those wages and deposit those withholdings with the IRS. It will be up to you to file a tax return and claim a refund, if a refund is due.

Since we are assuming you (the one who renounced your citizenship) do not have any income, we don't care about the withholding rules.

3. The filing rules

The election also applies the rules of Internal Revenue Code Sections 6012, 6013, 6072, and 6091 to the nonresident alien. See 26 C.F.R. §1.6013-6(a)(1).

These are merely mechanical rules that tell you what, when, and where to file when you are inside the U.S. tax system:

• Section 6012 lists the people who are required to file income tax returns (including the minimum amounts of income required to file, etc., thus answering the question "do I even have to file a tax return at all?");
• Section 6013 allows a joint tax return for husband and wife (this is the "what do I file?");
• Section 6072 contains the filing deadlines ("when do I file?"); and
• Section 6091 contains the rules for where to file tax returns ("where do I file?")

Why make the election? MFS vs MFJ

Let's look at why you would want to make the election. You will only make the election to be a U.S. taxpayer if you think it will save you money. This is usually because of the difference in tax treatment for married couples who file "married filing separately" as compared to "married filing jointly."

Fortunately, math will give you the answer to this. Every tax return preparation software package will allow you to figure this out.

My bet is that when you run the numbers, the marginal tax savings will be small. Maybe several hundred dollars, maybe a few thousand at best.

Why make the election? Section 1041

If you can't tell, I am unimpressed by the cost/benefit of saving a few thousand dollars on a joint tax return.

However, there is a definite strategic advantage to making the election when you want to move assets between the U.S. citizen spouse and the spouse who renounced citizenship.

Example

Let's say that a husband (no income stream, renounced U.S. citizenship) and wife (has the income stream, is still a U.S. citizen) have two jointly owned assets. One asset is a piece of real estate, worth $500,000. The other asset is a bank account containing $500,000 of cash.

For reasons known to the two of them, they want the husband to own the real estate, and the wife to own the cash.

Hint: let's pretend the wife is the U.S. citizen and the husband is the one who renounced U.S. citizenship, and let's further pretend that they live in Dubai, where there is no income tax.)

Without the election

Ordinarily, transfers of property between spouses will not trigger any tax. That's what Internal Revenue Code Section 1041(a)(1) says.

However, if one of the spouses is a nonresident alien, the special rule (no tax for transfers between spouses) will not apply. See Internal Revenue Code Section 1041(d).

First look at the "without making the election" scenario. If the husband gets a deed to the real estate as his sole property, and the wife gets 100% ownership of the bank account, this is the equivalent of the U.S. citizen wife selling her half of the real estate to her husband (a nonresident alien because he renounced U.S. citizenship) for $250,000 cash.

The U.S. citizen wife, in that case, will pay capital gain tax on the "sale" of half of the real estate to her husband.

With the election

Now let's pretend that our renouncing U.S. citizen makes the election under Section 6013(g) to be a U.S. taxpayer. This makes him a "resident alien" for purposes of "Chapter 1" of the Internal Revenue Code. And guess what? Section 1041 is in Chapter 1.

Let's re-apply the rule of Section 1041(a)(1) to the scenario.

The U.S. citizen wife transfers 100% ownership of the real estate to her husband, who is no longer a citizen but is a "resident alien" for purposes of income tax computations.

The husband transfers 100% of the bank account to the U.S. citizen spouse.

This is a tax-free event because the husband is a "resident alien" which means that the rule of Section 1041(d) does not apply to this scenario:

Subsection (a) shall not apply if the spouse (or former spouse) of the individual making the transfer is a nonresident alien.

Well, the spouse of the individual making the transfer is not a nonresident alien. One spouse is a U.S. citizen, and the other spouse is a resident alien. We can apply the default rule of Section 1041(a)(1) and this transfer is tax-free.

Why would you want to do this?

Simply put, you would do this in order to re-balance assets between the U.S. citizen spouse and the spouse who renounced citizenship. The objective would be to get all of the highly appreciated assets into the name of the nonresident spouse, and get cash into the hands of the U.S. citizen spouse.

Make the election. Do the rebalancing of assets. Then revoke the election. Have the expatriate spouse sell the assets without capital gain.

In my example, the wife ends up with $500,000 cash, and the husband ends up with the real estate. If he terminates the election to be a resident alien for income tax purposes, he can then sell the real estate tax-free.

Basis

The transferee spouse has basis in the property received that is equal to the transferor's basis in the property transferred. See T. Regs. §1.1041-1T(d), Q-11 and A-11.

That means the U.S. citizen spouse who holds the $500,000 of cash will have basis of $500,000 in that cash.

The husband (who renounced, then made the election under Section 6013(g) to be a resident taxpayer again) will have whatever basis the wife had in the real estate.

When he sells the real estate, he will be taxable on all of the capital gain. But he will cancel the Section 6013(g) election, and no longer be a U.S. taxpayer. The fact that this capital gain is taxable means nothing to him.

Gift

There are special rules that apply to gifts by U.S. persons to noncitizen spouses. We don't have to worry about these special rules. Let us concede that the rules apply to this situation -- and the transfer of real estate by the U.S. citizen spouse to her non-citizen husband.

The transfer is not a gift. It cannot be a gift from one spouse to the other, because fair market value was given in return: the wife transferred $250,000 of real estate to her husband, and the husband transferred $250,000 of cash in return.

How much did the wife give away, getting nothing in return? Zero.

A “gift” is any transfer for “less than an adequate and full consideration in money or money's worth.” 26 U.S.C. §2512(b). The transaction I described is one in which each side received money or money's worth exactly equal to whatever they gave up.