How do you move out of a house without deleting furniture?

You can go to the Manage Worlds, click on your household, click on three dots and then on the house with an X button. This will evict the household, meaning they'll move out and leave all the furniture there. Your household will be in the Manage Household panel. You can find it in the upper right corner (family with pencil icon). You can move them in somewhere else or delete them. You can also make them unplayed so they can take on the service sims' roles.
Just a tip: After that, go back to the house and remove all the objects that require to be unlocked with careers. If there aren't any, make at least one change (either add or sell furniture. You can sell a furniture and buy it back). Otherwise you can't buy furnished house with the new household.