My dad and mom told me to empty their safe deposit boxes immediately on death. This is one time I am glad I listened, well listened early. My sister and I did this a few weeks ago. We saw the writing on the wall. Last week I went to cancel the now empty box. The bank officers told me it was frozen and would need to go through probate. Thankfully, they looked (with us), saw that it was empty and let us hand in the keys. One less thing to worry about in the future.
I never dreamt that would be any kind of problem. My dad made sure to put both of us on the box. What no one realized is that we were on as deputies, not renters. As deputies, after death, we had no rights. We had never heard this, but now that I am aware, I will check the status of my children in my bank. I don't want them having any future problems that can be avoided.