If you or a permanent you control assembles a Contraption and your Contraption deck is empty, nothing happens. You don't lose the game.
Twiddlestick Charger
Contraptions aren't put into your main deck. They go into a separate deck called the Contraption deck.
If a Contraption would leave the battlefield and go to any zone other than exile, it instead goes to the scrapyard, the Contraption deck's version of the graveyard. Things that affect the graveyard do not affect the scrapyard. You can exile Contraptions just fine.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Ralph Horsley
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
