Welcome to Android Central, I think we may need a bit more information in order to offer you advice.
What device do you have?
What app are you using that gives you bells next to conversations?
I this something that has recently started, or has it been going on for some time?
Have you noticed that you are not getting notifications for the conversations with the bell and slash?
It sounds like the thread involving the bell with a slash are ones that have been silenced, a bell with a slash usually signifies that the notifications for the item have been turned off or the item has been silenced. So I would check the settings for that thread. For most SMS apps you would open the message thread and then open a menu for the conversation, three dots in one of the upper corners usually, and in the list of items see if there is one that says "turn on notifications", "unsilenced conversation" or something along those lines. Usually this is an intentional act but it could also happen if the device was in a pocket or something and the conversation was open or opened. The equivalent of a butt dial. Unfortunately I cannot really offer much more advice without the answers to my questions and for you to reply with those answers and any other information you may want to share you would have to create an account and become a member. Once you've created an account you will be able to reply to this thread. Please do not reply by starting another thread.