After months of waiting, Fida Ghanem was granted a permit by Israel and Egypt to leave Gaza for urgent lymphoma treatment in the spring. But the next morning, Israeli forces seized the only border crossing from Gaza to Egypt, in Rafah, as part of a military offensive against Hamas in the area.

Ms. Ghanem, 42, died one month later in early June. The border was still shut.

“She should have been allowed to leave as soon as they found the cancer,” said her husband, Maher Ghanem. “But it was delay after delay.”

For nearly all Gazans, the southern Rafah crossing has been the only way out since the war began nine months ago. But since Israel captured it in early May, it has been closed to all civilians and Israeli, Egyptian and Palestinian officials have been unable to agree on the terms to reopen it.

Aid workers and doctors have warned that the prolonged closure is endangering some of Gaza’s most defenseless, including children with severe burns, cancer patients and people needing heart surgery. More than 10,000 people need immediate medical treatment outside the enclave, according to the World Health Organization.

“The most vulnerable residents of Gaza — its children, sick, and elderly — are paying the highest price,” said Tania Hary, who directs Gisha, an Israeli human rights group that advocates freedom of movement for the more than two million Palestinians in Gaza.