I always advocate either creating a paper trail for future generations of genealogy or following a paper trail when trying to find someone who is deceased.
A friend of mine is going through a close family member being placed in a hospice center. When I worked for a church years ago, we had a list of things that a person who is the caregiver should do ahead of time in order to have as smooth a transition for themselves and their family member as possible. I am going to include it here as I feel it would provide a lot of places to look for hints and clues about their ancestors. Enjoy and good luck in your search.
Hospice Care Checklist for Family Members for End of Life Care and Aftercare.
The most loving act that a person will do for another person is the planning and execution of funeral and aftercare arrangements. No longer is the person there to give approval. It is strictly an act of love, obligation and respect that allows a survivor to complete the plans of the funeral.
Pre-planning for Funeral and Burial
24-72 Hours After Death
One Week After Death
Months After Death