A proposed solution to this dilemma involves the use of fraud proofs within a withdrawal protocol, which would enable multiple users with insufficient individual funds to collaborate off-chain and collectively perform a single, larger withdrawal from a pooled Unspent Transaction Output (UTXO).

Fraud proofs are designed to substitute expensive on-chain computations with claims that certain results will be produced, provided there is a way to contest fraudulent claims and penalize any fraud attempts. This method benefits from not requiring the full witness data necessary for the computation—instead, a simple commitment suffices as long as other parties can independently compute the correct data. The trade-off for using such optimistic protocols centers around needing a challenge period and assuming that miners do not censor challenger transactions. An example of an optimistic protocol in Bitcoin is the Lightning channel's "justice transaction."

In scenarios where a layer 2 system's UTXO stores user balance states and an operator or participant group updates these states, when something goes wrong, the system enters an "unwind" phase. During this phase, the only action permitted is for users to withdraw their money. High-value users can withdraw instantly by providing Merkle proof of their balances, while low-value users are unable to do so due to the cost of publishing the proof. To address this issue, a cheaper alternative is suggested: an optimistic withdrawal using a fraud proof. Users claim their balance and the remaining pool value, post a bond, and wait through a challenge period. If unchallenged, they retrieve their money and bond; if a lie is detected, the bond is partially seized and partially burned.

Further extending this concept is the optimistic aggregated withdrawal, where a subset of users authorize an intermediary, Ingrid, to withdraw their combined balances. Ingrid claims the total sum on behalf of the users, posts a significant bond, and awaits potential challenges during a time-locked period. If no issues arise, Ingrid can return the funds through various means, potentially custodially.

The outlined system has several notable properties. Intermediaries can be chosen at any time post-creation of the UTXO, encouraging user cooperation to find intermediaries who have yet to withdraw. The costs for claiming funds remain relatively constant, discouraging unsuccessful fraud as it results in financial loss. Additionally, any group of users with a sufficient combined balance can utilize the optimistic approach for withdrawal.

Some areas identified for improvement include a non-custodial role for Ingrid by pre-programming the destination of funds after the withdrawal and exploring a withdrawal protocol with constant cost regardless of the number of users. There are also open problems such as achieving parallel optimistic withdrawals without interference and determining specific script requirements.

In conclusion, while many details still need to be refined, the approach appears to be theoretically solid and awaits further comments and development.