WILMINGTON, Del. — If the Delaware Art Museum has a signature painting, surely it is Howard Pyle’s “Marooned.” A native of this city, Pyle is justly remembered as the father of American illustration. His “Marooned” (1909) is an image of genuine drama and distress. It shows a pirate near death, curled up on a sand bar, a tiny figure enveloped by a burning yellow sky.

The painting refers to the old custom of punishing insubordinates by shoving them off a ship and onto an island. But these days, you can also view “Marooned” as a curiously precise description of the Delaware Art Museum. It, too, has been ostracized by its peers. In June, it was formally sanctioned by the Association of Art Museum Directors, which has asked its members not to lend artwork to Delaware or assist with its exhibitions.

The spanking came one day after the museum sold a painting from its collection, William Holman Hunt’s “Isabella and the Pot of Basil.” Trustees say that the sale was the only way to help settle a $19.8 million expansion debt and plump the museum’s endowment. Now, for the first time, the museum is confirming that it will sell two more works. The first, Winslow Homer’s “Milking Time” (1875), is a masterpiece of American genre painting, a quietly intense farm scene in which a mother and son turn away and gaze over a wooden fence that seems to say something about held-back emotion. The Homer will be offered in a Sotheby’s auction this fall, unless a buyer turns up first. “That is our plan of attack,” Gerret Copeland, the chairman of the Delaware Museum board, explained. “If we find a private buyer, it will go sooner.”