I've tried this on two different computers in two different worlds, both in hardcore and survival. If you leave anything in a furnace when you pause play or save and exit, the contents disappear.
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I can also confirm this.
The problem also exists with servers.
As soon as something is finished in the furnace and it is not retrieved, the content is gone as soon as you leave the server.
If you leave the server before the process (there must be nothing in the output) is complete and the chunk is no longer loaded, the items are still inside.
The fire animation also remains. Even if there is nothing left in the furnace.
Duplicate of MC-277144.
Can confirm. It has happened to me as well. When reloading the world, the furnace continues to be lit, but is empty and items are unretrievable.