I send cards for birthdays. I would look for one with an appropriate message, like "Thinking of You On Your Birthday," not a funny card, or one that said something insensitive like, "Hope this will be your happiest birthday ever." [I remember getting one like that after my wife died.] There have been times when I could not find a birthday card I felt comfortable with, so I chose a blank card with a nice picture on the front, and wrote my own note.
The same awkward situation can arise when it's time to send Christmas cards. There have been times that someone on my list has had a recent death in the family. I keep several Christmas stock cards on hand that have different winter scenes on the front but no inside text, so I can write my own message in that case. I also buy regular Christmas cards that do have a standard Christmas message inside. Those go out to most people on my list.
I don't want to forget people just because they've had a great unhappiness arise in their life. That's the time they need to be remembered the most.