I've been though the exact same thing. Even made a thread about it.
In my case my friend had been my best friend for nearly 40 years. She then ghosted me. I tried to reach out, but nothing.
Her husband came round to see me, and wanted to know why we weren't speaking anymore, but I couldn't answer (although when they'd split up for a while he tried it on with me and openly told her he fancied me from when he met me -around 5 years after I met her, she seemed unbothered by it).
A few years later I got married, she found out and was around again, it was amazing having my best friend back, but she again ghosted me, shortly before DD1 was born.
I found out from mutual friends that she had cancer. All our mutuals thought I'd know as they knew we were best friends and always together.
I found out from her brother she'd died. I'm still really upset about it. Som many things left unsaid and I really did love her and she was a massive part of my life.
I didn't reach out to her. As much as I was tempted, the truth is it would have been for my benefit, not hers.
If your friend wanted to see you, she would reach out to you.
Don't make her illness about you, as much as you feel you want to support her, it may well come across differently to her.
The card is a nice idea, but if she's but you off, even that could be triggering.