If Federal taxes weren’t taken out in 2020, can a company rectify that and take out the 2020 Federal taxes?

Any money your employer withholds from your 2021 paychecks will count towards your 2021 tax. Even if they could somehow count it towards your 2020 tax, you would still owe the penalty for paying so late. 

What you CAN rectify is how much they withhold from now on. 

Not after 2021 starts

The money is owed by you one way or another dick head. They would have to extract the money from your future salary to cover it. There is no magic bean where they will just give the government some of their money and you will get a refund. It is tax money owed by YOU! And it is your responsibility to review your pay stub to ensure that you have directed the company to take out the correct tax!>!>!>!

Not possible.  If it was, your company would ask YOU to write them a check, then forward it to the IRS.  The company doesn't have the money, you do.

Sounds to me like your sister isn't a tax expert and you should ignore any advice she attempts to give you regarding taxes. Her proposal is completely wrong and is simply not possible.

There's no way for the company to retroactively withhold money toward last year's taxes.

In most situations if you did not have enough tax withheld its because you filled out your W4 form incorrectly. Even if the company payroll department did make a mistake and compute the withholding rate incorrectly, you have the opportunity every payday to review your pay stubs and turn in a new W4 to make changes if necessary.

So the bottom line is that you and ONLY you are responsible for ensuring that your taxes are paid in full and on time. If the money isn't withheld directly from your paychecks then you get bigger paychecks but you must take responsibility to use that extra money to pay your taxes.

The only thing left to do now is file and pay what you owe. If you can't afford to pay the whole bill then file, pay as much as you can right now, and set up a payment plan to pay down the rest of the bill.

Meanwhile make sure you change your W4 so that this doesn't happen again for 2021.

If you still owe a balance for 2020 taxes when you file your 2021 return, then any refund for 2021 will automatically be applied to the debt from 2020.

Well no, because you already have the money.  The company is not paying your taxes for you.

No.  She is wrong.

2020 is done.  What was withheld for 2020 is what was withheld for 2020.  It can't be changed now.

You have 2 options:Option 1)  Make arrangements to pay what you owe; or,

Option 2)  There is no Option 2.  Please refer to Option 1.

Anonymous is correct, except on item 3, they mean your W4 is correct not your W2.

Also, check your paycheck each period against paycheckcity.com to make sure you have the appropriate amount of taxes withheld.  .

No she is not right.

1)  You have already received your pay from your employer for 2020 so there is no longer a mechanism for them to deduct anything; and

2)  A tax refund is what you get when you overpay your taxes.  If you underpay your taxes, you simply write the IRS a check for what you owe.  

3)  Make sure the W-4 you have filed with your employer is correct so that your employer withholds the appropriate amount of tax.

ETA:    Yes, edited to correct W-2 to W-4.    And I agree with the recommendation to look at every pay stub to ensure it's correct.