The short answer is yes but there are several conditions to the continued processing of the application notwithstanding the death of the petitioner. The beneficiary must also be eligible to adjust status in the US or, he might have to be consular processed notwithstanding the new law. I will need more details to assess whether the person is eligible for adjustment of status. If s/he is not eligible there are other options to avoid removal proceedings.
You may be eligible to adjust status if you do not have inadmissibility issues and fulfill the requirement pertaining to adjustment under these circumstances.
It has been done in several similar situations.
You are welcome to contact me to discuss the facts of your case if you wish and find a way forward.
Time is of the essence.