Plasma
Plasma was an early (2017) Ethereum scaling design that ran transactions on a faster child chain while periodically committing only a compact Merkle root of the child chain's state to the main chain. The promise was rollup-like: most activity happens off the expensive base layer, but users can always fall back to Ethereum to prove ownership and withdraw their funds. It was a major conceptual step on the road that eventually produced rollups, and OMG Network and early Polygon used Plasma-style constructions.
Because Plasma posts only state roots and not full transaction data to Ethereum, it relies on fraud proofs and an exit game to keep operators honest. If the Plasma operator publishes an invalid state, a user can submit a fraud proof to challenge it; to leave the chain, a user starts an exit referencing their funds, waits out a challenge period during which others can prove the exit is fraudulent (for instance because the coins were already spent), and then withdraws. This is similar in spirit to optimistic rollups, but with a fundamentally weaker data model.
The fatal weakness is the data availability problem. Since transaction data lives off-chain, a malicious operator can withhold it — publishing a valid-looking root while hiding the underlying transactions — so users cannot construct the proofs they need to exit correctly. The defensive answer is the mass exit: if data is withheld, everyone must rush to exit at once, which the base chain cannot process quickly and which becomes chaotic when users do not even know their current balances. Plasma also struggled to support general smart contracts, only ever working cleanly for simple payments and token transfers (Plasma Cash). These limits are exactly why the ecosystem pivoted to rollups, which solve data availability by posting compressed transaction data on-chain; a leaner Plasma revival has been explored but it remains largely historical.
Plasma and optimistic rollups both use fraud proofs and exit windows; the decisive difference is where the data lives. Plasma keeps transaction data off-chain (so withholding breaks safe exits), while a rollup forces it on-chain — that single change is what made rollups practical for general computation.