I have always valued any things, not just jewellery, left to me by family members. When I married my second husband, I asked my mother if we could use her mother's wedding ring. (She said, "Of course" and I still wear and treasure it although it is worn paper thin since it went on her finger in the late 19th century. I have and often wear other family jewellery, some of which is quite valuable.
However, a few years ago my daughter was in dire financial circumstances and I was not, at that time, in much of a position to help her out. I had a pile of family wedding rings, including my mother's, that I had also inherited from various aunts. I was never going to wear any of them and I don't need "things" to remind me of those I love who are no longer with me. I gave them to absent daughter and told her to sell them, which she did for a surprising amount of money.
When you give someone something, or they are given something by someone else, it is their's to keep, to give to someone else, to sell. You do not have a say in the matter.