We’ve made an update that addresses both of these problems:
If you have setup a tag as an Enable solved tag, removing that tag from a solved topic will remove the solution. We’ll notify admins when they go to remove the tag so they’re aware:
In situations where the topic is in a solved category and has a solved tag, removing one or the other (i.e. removing the solved tag but keeping it in the solved category or moving it out of the solved category but keeping the solved tag) has no impact on the topic’s solution.