The sentence "I am safe" is correct and usable in written English. You can use it when you want to reassure someone that you are safe and sound. For example: My friend texted me to check on me during a natural disaster, and I replied, "I am safe.".
I am safe where I am".
Now I think I am safe, for the time anyway.
He added: "I can assure you that I am safe and sound.
("As soon as my feet hit the stage — I am safe," she wrote).
"I am safe and sound and living in a safe place".
As I said, I am safe and on the run and always looking after myself".
"I am safe now," he said, tearfully, from the food-delivery window.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union