I feel like my cat's death is my fault. I'm so sad, how can I possibly forgive myself?

About two years ago I gained the trust of a stray cat that lived outside of my boyfriends house. We bonded to the point where this cat went from sprinting away from the site of any humans to purring and hopping onto my lap to cuddle. She was already really old when I befriended her and too skinny to be in full health. I tried to gain her wieght back by regularly feeding her wet food but nothing worked. She seemed happy though, so I just tried to make the rest of her life one full of love, since she had been alone for the entirety of it until I befriended her. Well, my boyfriend went on a trip for 6 days and I was so busy i didn't go over to spend time with the kitty. I really should have. My boyfriends parents left food for her to eat in the house and everything so she wasn't starving but it was dry food, which she wouldnt eat as much. It was really stormy while my boyfriend was gone, like 4 inches of rain an hour, and i thought the cat would be fine because she lived her entire life as a stray and she could go into the house if she wanted to (she slept outside). But then i got a call from my boyfriends mom, who knew I loved the cat, and told me the kitty was really sick and that we had to put her down. When i got there, she couldnt even walk, there was no strength left in her. I put her in my lap and she didnt even have enough strength left to purr, she could only slightly nuzzle my hand when i put it up to her face. It was so unbelievably heart breaking. My boyfriends mom is positive it was cancer. I know she wasnt at optimal health and didnt have much longer to live, even before she got super sick she was skin & bones, lost her balance alot while walking and sat down slowly like her legs might give out, but I feel so much that her getting so sick so quickly is because i wasnt there for her during the stormy weather over the 6 days.There was thunder and lightning too and she didnt go inside so she was probably somewhere outside scared and cold. The aread she normally sleeps at outside was all messed up so there was no shelther for her so she had no where to go over those 6 days. No one else in the family takes care of her and it's all my fault she got sick because i wasnt there for her! I'm so sad and I miss her so much and regret more than anything not being there for my kitty. I feel like she got sick because of me. I know she was old and not at optimal health, but I should have gone over to my boyfriends house while he was gone to take care of her. Maybe if i was there to coax her inside and feed her wet food she would still be here. I'm so sad and there's nothing I can do. In the end, I wasn't there for the cat that trusted me and only me, her only friend throughout her entire life. I know it's just a cat but it was an extremely special and rare bond i gained with her, it's not every day a cat goes from living 14 years as a stray to running up to you and meowing to be pet. I'm so sad. We had to take her to the humane society to be put down because a private facility would cost over $200 dollars. So we took her in, i was carrying her curled up in a little box. But then the humane society told us we couldn't even go in and hold her while they put her down. This broke my heart even more. Being a stray cat, she's still wary of strangers and I wanted to be there holding her while they did it. It's not like she'd fight them or try to get away, she was so sick already all she was doing was lying there, but I wish I could have at least been there for her in the end. I'm so heartbroken about the whole situation, I can barely see what I'm typing through my tears. I know my friendship gave her a better life, but I feel like I failed her in the end.