I removed all the tables from my village and yet like half of the villagers didn't lose their jobs. There are villagers in which both villagers would get the same job from a single table and when one broke it one would lose the job and the other would keep it.
There is a taiga biome mapper which only retains the texture of the mapping work but cannot be traded and you cannot be reassigned any new work either.
In the photo "17545821782104634436517253050243.jpg” Which is the last photo taken, You can see a farmer villager who does not have a work table but does work.
If a villager has been traded with once they will never loose their job profession. Some of the villagers in the screenshots have level 2 and 3 (iron and gold belts). It is only the villagers who have never been traded that can change their job