The IRS does have the authority to write off all or some of your tax debt and settle with you for less than you owe.
This is called an  "OFFER IN COMPROMISE", or OIC.

But beware: OICs are usually rare

In fact, there are more than 16 million individual taxpayers who owe the IRS – but in 2017, only 25,000 got an OIC. Most people are better off requesting other IRS options, like IRS payment plans, or “ currently not collectible status ” – where your allowable expenses exceed your monthly income.

You’ll have to prove you can’t pay

To qualify for an OIC based on “doubt as to collectability” (that’s IRS speak for, “You owe, but you don’t have the money to pay.”), you have to prove to the IRS that it can’t collect all the taxes you owe before its time runs out. This deadline is called the collection statute expiration date , and it’s usually 10 years after the IRS charges you (or, “assesses”) the taxes.

Practically, this means that your net equity in your assets (home, 401(k), savings, investments, etc.) plus your monthly disposable income (your average monthly income minus your allowable monthly living expenses) is less than the tax you owe.

The IRS determines your net equity in assets and monthly disposable income using specific rules to value your assets and determine what living expenses are allowed .

OICs can get complicated

Even if you qualify for an OIC, remember that you still have to be able to pay the amount needed to settle the tax bill. This is called the “offer amount.” This amount often largely depends on the value of your assets. People who have built up equity in their home or 401(k) may have to pay their “net equity” in these assets to the IRS as part of their offer amount.

The offer amount also includes what the IRS will receive in monthly payments over a certain period of time. The amount of time depends on several factors, including how long the IRS has to collect and the payment method you’re using to pay the offer amount.

For many people, a payment plan or hardship status is likely a better option.

How to evaluate the OIC for your situation

The IRS offers an option for you to evaluate the OIC, called the OIC Qualifier tool. This tool does the basic qualification elements of an OIC, but doesn’t account for many of the nuances in calculating value in assets and average monthly income and expenses.

Likely, you’ll need a tax expert to help you determine your assets, liabilities, income, and expenses, as well as other factors that help determine whether you qualify. If you do qualify, your tax pro can determine how much your offer amount should be, and deal with the IRS for you to request the OIC. If not, your tax pro can also help you request the right IRS payment agreement for your situation.