How does a museum decide to dissolve?

That question could ultimately face two cultural institutions: the Detroit Institute of Arts, whose artwork may be sold off because the city has declared bankruptcy, and the South Street Seaport Museum, which is desperately trying to stay afloat.

Museums don’t often go out of business. They cut back, they pare down, but they tend to persevere as cultural anchors of their communities. And neither of these institutions has announced plans to close; both are hoping to weather their current storms.

But both are arguably in jeopardy — the Detroit Institute because a sale would denude its prestigious collection of its most valuable artworks and compromise its integrity, since nonprofit museums, founded in the public trust, are ethically obligated not to sell pieces except to acquire others; the Seaport because it has struggled for years to pay its bills and recently lost its white knight when the Museum of the City of New York said it could no longer afford to run the museum, which was damaged by Hurricane Sandy.