A portion of a dish left by the guests, that the host may not feel himself reproached for insufficient preparation.--Joseph Hunter's Hallamshire Glossary, 1829
A morsel left in a dish to avoid the imputation of greediness.--T. Ellwood Zell's Popular Encyclopedia, 1871
Bank Holiday (Scotland)
Feast Day of St. Macarius,
a fourth-century patron of cooks. The anonymous English author of Don't: A Manual of Mistakes & Improprieties (c. 1880) confirmed the old manners-bit custom mentioned above, explaining, "Don't devour the last mouthful of bread, the last morsel of food. It is not expected that your plate should be sent away cleansed by your gastronomic exertions." But in the latter nineteenth century, according to Alfred Ayres' The Mentor (1884), a new paradigm developed in which taking the last tidbit was encouraged as a means of displaying confidence in one's host: "Do not hesitate to take the last piece on a dish or the last glass of wine in a decanter simply because it is the last. To do so is to indirectly express the fear that you would exhaust the supply."
See also "nobody ever wants the last cookie/slice of pizza". But I gotta say, in re: reading "you don't have enough food" into taking the last whatever, it sounds to me like some of those 1880s hosts were looking for things to get offended about.