Minerals (or at least the visual on the knight's back) can be carried over cross levels under the following circumstance:

• A knight joins the game and has their player spawn into a party already on the elevator, delaying the elevator's descent.
• A mineral is able to be and is picked up from the point they have spawned at before the elevator goes down to the next floor

I've personally forgotten if the mineral acted like a standard mineral from the level, but it may have.