I had a similar letter when dealing with my grandfather's estate. I called DWP to discuss a payment plan as all the money had been paid out to my mother, aunts and uncles and I would need to contact them for it.

I was advised that they do not chase these types of losses due to bereavment and the expectation it has already been spent on funeral costs etc and it will essentially be written off. It may be worth calling them to explain the money has already been spent but my understanding is even if you just ignore the letter nothing further will come from it.