I'm the crappy neighbor.
DH and I saw that the house down the street from us was for sale so we wandered down to grab the info flyer out front of the house. The lady who lives there came out to say hello (we've spoken once when we moved in two years ago so she recognized us). As you can tell, we're not very social with neighbors.
She said to come in and see the house if we were interested and as she was showing us around, she'd say things like "this is where my husband kept his guns" and "my husband just put this new door on". I couldn't tell if she was divorced or if her husband had passed, and I wasn't about to ask in front of her kids who were playing around us.
Later, DH and I looked them up online and found out that her husband has just died in a fiery plane crash TWO WEEKS ago and it was all over the news. I just didn't know it was him. I felt so horrible. I didn't know so I didn't say anything like I'm sorry for your loss or at the very least, how are you doing. We just gushed over how much we loved the house.
Do I send her a card? Skip over it completely? Either way seems awkward, especially since we might be buying her house. Also, I'd have to explain how I found out, which is embarrassing.
Re: Crappy neighbor. tl;dr
Did she realize you were the neighbors when she was showing you around the house? I think either way, I'd send over a card and I think VERY soon, like today or tomorrow, bring over a casserol or order them a pizza or something. You didn't know, but you do now, you know? You can just say, "I'm so sorry for your loss. I didn't know at the time when we stopped by, and I want to offer my apologies if I came off as insensitive to you in this time of grief." or something to that extent.
If she didn't realize you were the neighbors when you stopped by I think I'd still send a card and food but just send your sympathies with the card, don't bring up the awkward house showing.
I do think I'll send a note and a dish. I agree, @BPaws, everything you wrote was perfect GWP - thanks!