What does Boxing Day have to do with boxing?
c.1200, from Old French begart, originally a member of the Beghards, lay brothers of mendicants in the Low Countries, from Middle Dutch beggaert "mendicant," of uncertain origin, with pejorative suffix (see -ard). Cf. Beguine. Early folk etymology connected the English word with bag. Form with -ar attested from 14c., but begger was more usual 15c.-17c. The feminine form beggestere is attested as a surname from c.1300. Beggar's velvet was an old name for "dust bunnies." "Beggers should be no choosers" is in Heywood (1562).
"reduce to poverty," mid-15c., from beggar (n.). Related: Beggared; beggaring. Figurative use by 1640s.