Sorry for your loss.
If you have entered what you have access to in TurboTax to prepare a return for your parent, you can use what TurboTax states for 'tax liability' when filling out your Extension Request.
The IRS states to 'estimate using the information available to you'. If you have no idea whether there is a Tax Liability or not, enter $0 for that question.
If you know there is a Tax Liability, you can pay the amount by April 15 at IRS Direct Pay, (even if it will change later), which will automatically give you an extension.
More info:
https://ttlc.intuit.com/replies/3301811