MTG How cypher works on mishra's factory?

I think you are misunderstanding how Cypher works.

When you cast a spell with Cypher on it (Undercity Plague for example), as it finishes resolving, you may exile that Undercity Plague encoded onto a creature you control (Mishra's Factory in your example). From then on, whenever that Mishra's Factory deals combat damage to a player, its controller may cast a copy of the exiled Undercity Plague without paying its mana cost. It does not let you cast copies of Mishra's Factory..