Grief is personal and bizarre. It's best to let your loved one guide you through their needs, often just listening.
Making sure they have some nourishment is important,
Making a phone call just to say hi is nice too, without being morbid.
Perhaps talking about what needs to be done is important too and offering to help.
Spend 'empty' time with them, just being there, doing the ordinary life-time sorts of things with them, like making a cup of tea, lighting a fire, feeding the pets, making beds.
If they have been deserted, it's important to just commiserate by listening to their grief, without denigrating.
Keep it up regularly so they know they can depend on you for solid and sensible friendship.
"Sensible" is the operative word in insane making times.