So first step, if you plan on filing her final tax return, you have to go to court and be appointed as her estate's representative or executor. The fact that you were her proxy doesn't carry over after death, and neither does a power of attorney. For a small estate, it's probably a simple form to file with the court.
Next point, you can't sell or distribute any of her assets until all her final bills are paid and that includes taxes. If she owes more than she can pay, no one else in the family is responsible, it just goes unpaid. But you can't distribute other assets until all the bills are paid.
To your question, it's not clear why there would be a penalty for back pay. Do you mean income tax?
There are three things I can think you might mean.
1. You might mean, she got a large lump sum payment and will owe income tax, how much is it? Unfortunately you need to actually file the return to find out, although you can make some estimates using this tool.
TaxCaster tax calculator
For most people, income taxes are 24% or less. It would have to be a truly enormous payout to be taxed at more than 24%.
2. Or, you might mean, since she got a lump sum of income and did not pay estimated taxes, she may owe a penalty on her tax return in addition to the income tax. The penalty plus interest is about 1% per month of the tax amount owed. For example, let's assume a $50K lump sum disability income payment made July 1, and she has no other income. The estimated tax would be due September 15, about $5000 for this example. If you don't make a payment until February 15 when you file the return, the penalty plus interest would be $50 per month for 5 months, or $250 total.
You can limit the penalty by making an estimated payment now instead of waiting to file the tax return, the sooner you make the payment, the less the penalty will be. If you make too large a payment, the extra will come back as a tax refund.
You also have the option to not include a penalty calculation when you file, and wait and see if the IRS sends a bill. If the IRS sends a bill for the penalty, you can apply for a one-time waiver if this is her first time owing a penalty, or you can apply for a waiver for cause (like, she was disabled and didn't know a penalty needed to be made and you as her representative made the payment as soon as you realized it was owed).
3. Or, by penalty you might mean that after her death, some part of the disability payment must be paid back to the insurer. We have no way of knowing anything about that.
