A TX with zero fee will not be relayed by mempools. However, a TX with no fee can be added to a block.
Usually, zerofee txns are put there by the miner who mined the block. Maybe it's their own tx, or they got paid out of band to include it.
A TX with fee below a mempool's "purging feerate" will be dropped after about 2 weeks.
As long as blocks are full, its unlikely mempools/miners will permit any zerofee txns without some kind of reward.
What if the only change to BTC is that the fees come back down for a few days/weeks? Seems like then, the "poor people" could consolidate their UTXOs or open a LN channel.