If a spouse pass away, is it improper for the spouse's friend to ask the widow out?

If it's to help the family out with legal issues MAYBE but that's still a strong maybe. Otherwise, not right away. You should think of what would be a good amount of time for that person to cope with strong emotional Problems via from examples of their past experiences. I wouldn't use the death of their family dog dying as an example, more like their first home burning down because some nutt job thought fire looks pretty so it has to be an intense or extreme example. Ask too soon and it will come off a disrespectful to the deceased and the loved ones of them (that includes the spouse.) there may be exceptions if the dead spouse was an abusive uncaring person to either the spouse or everyone. But if you both hook up in privacy, depending on the family, might want to keep that on the down for a little while longer. If you try to use mind games to make the deceased spouse look like a bad person, even if you succeed, it will only last so long and usually never works out in the end and ruins your reputation. Other than that I don't know. I wish you the best of luck.