I always felt that it implied he'd never totally go away... just like the poor.

To me it also stood as a lesson in piety. You can decorate statues, annoint yourself (and others) with oil, make this grand show of being deferential to Pastors and Priests; when in fact, it's the little deeds that you do for the poor, unclean and forgotten people that mean more to Jesus the person.

One act of kindness is worth more than any oil of nacre or gold or silver.

LTS