I think some difficulties stem from the way leave is arranged. I recently lost a close relative, and grief for me feels easier split into small parcels of time, rather than trying to manage it all at once... and then what? He'll still be gone, it will still hurt next year and the year after, so that sadness needs to fit in with life and not overwhelm it. I took a day off immediately, another morning then afternoon later that week for funeral arrangements, another day the next week because I couldn't work that day, plus 3 days booked in for the funeral. I can't imagine still sitting about not working at all, and we have a child so life is continuing regardless, but I might take other bits of time off too. Most work is getting done and nothing gets too late because I'm not suddenly off for weeks, the benefit to me is that I can distract myself with work when possible and just stop when it isn't. Most people can't do that because of silly "number of absences" tracking prioritised over the number of days. On top of the admin, grief goes in waves, and I suspect it would help many people if there was flexibility for leave accordingly.
If the woman isn't able to work due to shock, then it is best for her to talk to her GP for a sick note and she will just need to manage that with her company. If it's the waves of grief and managing all the admin, then can she ask work for a day unpaid leave each week, so she has money for bills but also extra time on top of the weekends to sort things out? Just knowing she only has to get through 2 days at a time and Wednesday off for example, might make it easier. Getting and sending copies of the death certificate, birth certificate, passport, bill copies and whatever else is randomly required by the range of parties to inform about a death is time consuming too, but when the first few are done it becomes easier. Does she have any friend to help her organise things?