beggar, beg, give
匃 centers on the act of giving, especially in the context of begging or charity: a beggar asks for something, and someone gives it. The meanings 'beggar', 'beg', and 'give' are two sides of the same transaction.
匃 is a rare character. It combines 勹 (wrap, enclosure) with 亾 (an old form related to death or loss), but the exact historical development is uncertain. It may have originally depicted a person wrapped in poverty or loss, leading to the idea of begging.
The outer 勹 wraps around the inner 亾, which looks like a person with nothing. Imagine a beggar wrapped in a thin cloth, holding out a hand to ask for something to be given.
For カツ, imagine a beggar wearing a tattered coat, and a passerby gives him a cut of bread: 'cut' -> カツ, and the giving eases his hunger.