Round here, money is generally only given if it's known that there is a need for it. IE, an unexpected death (young person, etc.) so funeral expenses weren't planned for, or if the family is in bad financial circumstances. It's also usually given in a directed way, like, a check with a note explaining that it is to help with funeral expenses. Otherwise it seems like compensation for their loss, which is just.. weird.
Gifts tend to be more service-related, such as babysitting while family attends to funeral arrangements, or food of course, or household help. I've also seen gifts of "something to give you a break", like a spa visit or something like that.
But just handing someone money, when there's no indication that they need it, would be unusual.