The neighbor suddenly choked with sobs,her tears gushing from her eyes

这就是“独立主格”结构.
her tears主格
gushing from her eyes现在分词,表示主动、进行.
这个结构在句中充当伴随状语,相当于一个次要动作的.
可以写成：
The neighbor suddenly choked with sobs,and her tears were gushing from her eyes.
邻居突然哽咽起来,她的眼泪从眼中涌出.