I remember seeing an old idea but unfortunately I didn't bookmark it and now I'm struggling to find the source again. Maybe someone will remember it and be able to point me to the source?
It was something like:
Have a consensus (SF) rule that allows swapping 1-sat for a 0-sat UTXO which has the number of fractions recorded as something like
<fracSats> OP_DROP appended to the Script, e.g. 1-sat would convert to a 0-sat with
100 OP_DROP for 1/100 subdivision. Then, rules would enforce that these fracs add up correctly within the scope of the TX.
From PoV of old nodes, it would be a bunch of 0-sat inputs creating a bunch of 0-sat outputs, valid by consensus but currently prohibited by relay rules.
When someone collects 100 fracSats on the input side, they'd get a 1 full sat back on the output side, I don't remember how this was supposed to work without violating consensus of old nodes, maybe the UTXO would still be 0 but miners would copy the UTXOs locking bytecode in coinbase TX and credit it with 1 sat.