"Let me know if there's anything I can do to help." Yeah, you can start by doing instead of asking what you could do for the bereaved, and not wait for that person to tell you. Who feels comfortable even under less upsetting circumstances asking a friend to cook dinner for them, run errands, or clean the frickin' bathroom? Add to the mix the death of a loved one & reaching out for help could feel near impossible. This is all very easy for me to say as I sit thousands of miles away typing fitfully into my laptop. What am I doing to lend a hand? Nada.
I have one really bad-ass friend who, when very incapacitated a few years back, was able to reach out to her friends and say, "Look, I need help with keeping my apartment tidy, I'd also really love for prepared food items to be brought over to my place, and I may need help in getting to appointments now & again." I really respect that she was able to ask for what she needed. She is exceptional that way. The rest of us, when confronted with trauma, would probably tend to fold into ourselves, and not ask for help at all. May we all be proactive in helping those in need of a little extra support!