Thanks to everyone for your thoughtful comments. I do appreciate them.

For me, it would depend on what I understood of the person. A hug or two might also be appropriate, as already suggested by @mzee, @michelle666gar and @Betty. Also, listen to what the person cares to say, but do not feel impelled to say anything in return as a look of sympathy may be quite sufficient for the moment.

Depends on how well I know the person/people. A hug and I'm here for you or my condolences.

Expressions are a broad subject.

Apart from the excellent contributions noting deepest sympathy and heartfelt condolence.

Given it's "genuine concern" from godless heathens for those in "religious communities", I'd probably start with an ejaculation of surprise like "Oh no".

"Wally sorry to hear you fell asleep only to wake several years later to ask a question here at easter but hey resurrections are trending".

You'll be in my thoughts.

"My thoughts are with you during this challenging time."

I do not think there is or should be anything. What you should say is something unique and appropriate, to the person you are addressing and the person you are speaking of. The Christians "prayers" line is just an easy lazy get out, which merely shows that they don't really care or think.

If you can not think of something special to say, then it is perhaps better just to be silent and offer your support by just being there.

Tell them how you felt about the person and say so sorry for your loss, my deepest condolences and give them a hug. I recently went to a rosary for a lady who would take my classes and she passed away suddenly, I knew her and her husband since 2008 and they were both such a sweet couple. I couldn't believe she passed away, I cried by myself. Her rosary was beautiful but I left in the middle of saying the prayers of the rosary, I couldn't handle that.

That's rough buddy

Or anything remotely resembling empathy

me no talk, just give hug.

I recently attended a service for a catholic widow. After giving the eulogy for her late husband she asked, “Would anyone like to say a word for her dear late husband”!? I stood for a moment and said, “Plethora”! She said, “Thank you so much, that means a lot”!!?

Sorry for your loss.