the attempt to sustain the person is the cause of pain
Looking from a Buddhist perspective, attachment would relate to desire, or lust, or clinging. It is the latter that creates suffering, and misery, in the form of a desire, or lust to keep and perpetuate that which is not sustainable; include life - which we each know is unsustainable.
Ultimately it is not the death of a person that causes pain, rather the attempt to sustain that person. This pain is not the grief of their dying. Grief is the lament for their dying that unfortunately so often is consumed by the attachment to that which has gone.
We each may act as the Speaker For The Dead when someone dies. This involves the acknowledging of this person with honest reflection that speaks of all aspects of the person. So, this is not a case of 'speaking ill of the dead' rather an honest appraisal of both their faults and and their virtues; along with a recognition and recounting of our own interactions of joy and sorrow.
Attachment is most often about the memory, the what was. The memories can be treasured and enjoyed as much as they might be rejected and be distasteful; but so often there remains an attachment to the past experiences. To work on letting go of both the pleasure and pain of the past experiences releases you to a choice to recount a memory; to learn and grow; and to live the pleasure and pain of the present experience more fully.
What is past is gone, gone forever. Living in the past experience avoids living with the present experience and the present pain and grief. What generally happens over time is the person relinquishes the past experience due the impacting present experiences - 'you'll get over, just give it time'. This is the realisation of the unsustainability of clinging to the past experiences that are often confused as memories.
Memories are the remembering of past experiences. When we recall a past experience we bring to this our current reactions. For example, as I recall a past experience of my parent's death, I feel sad and tearful. My sadness shows as tears; and my thoughts are of a shared time together. This shared time could a positive or negative one. As a positive experience I lament at its loss; maybe wanting to relive the experience - and as such I live in the past, or I can live in the present acknowledging I want to experience this again in my current life; receive a similar positiveness. As a negative experience I similarly lament at its existence - living in the past, wishing and fanatasing for it to be different. In the present I can stop clinging to the fantasy and face the reality there was a 'me' that suffered and the 'now me' can sooth, empathise, and recognise now is different and take hope from this.