Jairus
Author of FFVII: Lifestream & FFVII: Reflections
They made it look like Biggs died in his last scene with Cloud, but he didn't. So I'm sure the same can be the case with Jessie. Maybe she just blacked out, like Biggs. Lost consciousness due to her injuries. Cloud and Tifa couldn't stay to be sure because they had to save the pillar, and they couldn't get back to her later when they came back to Sector 7. So they just assumed she and Biggs were dead. But they were wrong about Biggs, so they could've been wrong about Jessie, too.