This ruling notwithstanding, there are organizations in Israel today that maintain this Biblical concept in the modern age – see http://leket.org.il/english/text/305.aspx
We have learned (above, daf, or page 131) that in certain years farmers are obligated to give a special tithe to the poor. In addition a farmer is obligated to leave pe’ah – a corner of field – as well as leket – gleanings (grain that falls during the harvest) – for the poor on an annual basis (see Vayikra 19:9).
The Gemara on today’s daf relates:
Levi once sowed grain in Kishor, and there were no poor to collect the gleanings, so he came before Rav Sheshet. He told him: It is written: “Thou shalt leave them for the poor and the stranger,” but not for ravens and bats.
According to the commentaries, Kishor was a city outside the land of Israel, and the Hatam Sofer suggests that when Rav Sheshet ruled that there was no need to leave leket in the fields when there are no poor people to collect it, it is because the entire obligation is only obligatory on a Rabbinic level.
The Rema rules that even in the Land of Israel there is no obligation to leave leket, since – in his time – the majority of the inhabitants of the land of Israel were not Jewish. Based on this ruling, the Hazon Ish suggested that even in the modern age when there is a Jewish majority living in Israel we continue to rely on the Rema’s ruling. This is based on the fact that we know that no poor person would trouble themselves to collect gleanings in the field when staple goods are widely available and subsidized, making leket not worthwhile. No individual poor person would go to harvest leket or pe’ah, thresh the grain and grind it in order to make flour and bake. For that reason, leaving leket today is the equivalent of leaving it for ravens and bats, which Rav Sheshet ruled was without purpose.