ATHENS — While money pours out of Greek banks and Europe debates whether or not Greece deserves its next handout, the people potentially in the best position to help shore up the nation’s finances are mainly keeping their heads down.

They are among the wealthiest Greeks — whether shipping magnates, whose tax-free status is enshrined in the constitution, or the so-called oligarchs who have accumulated vast wealth via their dominance in core areas of the economy like oil, gas, media, banking and even cement.

Astute investors, they have been reluctant to lend a hand to the Greek treasury through the risky proposition of buying government bonds. But they have also been slow to dispense funds to philanthropies trying to combat the mounting social ills that their nation’s economic collapse has wrought — drawing a sharp rebuke from the head of a foundation created from Greek shipping wealth that has become Greece’s largest charitable donor in recent years.

Mainly, though, they have done what Greeks, from the richest to those of modest means, have traditionally done: pay as little as they can in the way of taxes.