“We can’t see them, because we have not just a fence — we have a wall around three-quarters of the kibbutz, so we don’t really see the border,” said Ms. Kissin, 49. “Sometimes I don’t want to know. If the army catches him seconds after he crosses the border, I don’t think I should know, because it really makes the tension more high.”

In Gaza, men who had crossed said Israeli security officials had questioned them, sometimes for hours, about whether Hamas or any other group had sent them, how they had planned their escape, what they intended to do in Israel and, broadly, what was happening back home in the war’s aftermath. When they returned to Gaza, they said, Hamas security officials questioned them, sometimes for hours, about what they had told the Israelis.

Iyad al-Buzom, the spokesman for Gaza’s Interior Ministry, said it had taken “serious measures to prevent border sneaking” since the war and was considering “more harsh procedures and punishments to stop those who think of crossing the fence.” He said officials worried that crossers would be pressured into revealing information to Israeli intelligence upon their arrest, or be hurt as they tried to get to the other side.

Data from the United Nations’ Office for the Coordination of Humanitarian Affairs show that Israeli soldiers killed six Palestinians near the fence in 2014, all but one before the war. That was double the number in 2013, but significantly fewer than the average of 22 annually in the previous four years. Thirty-nine Gaza residents were wounded by Israeli fire and tear gas from September through January, the data show, some while protesting or throwing stones, others while trying to cross.

Ateya al-Nabahin, 15, was shot in the neck as he tried to sneak into Israel in November, and he returned home in January after being treated in two Israeli hospitals. “Now, he is lying on his bed like the dead,” Ateya’s brother, Fadi, said in a recent interview. “He cannot walk or even talk like normal people.”

Looking back, Hasan and Salwa al-Zawara’a see plenty of signs that their 20-year-old son, Noor, was planning to cross before he disappeared Oct. 27 from their home in Johor al-Deek, a village next to the Bureij camp.

Three days earlier, his mother recalled, Noor asked for a copy of his identity card. That morning, he changed clothes several times before settling on jeans and a black shirt. He had almost never had a decent night’s sleep since the war, his father said, and he had been asking a sister’s husband who had spent six years in Israeli prison what life was like there.