你说的“无动词分句”，我认为可划分为两种情况：

①并非分句，而是一种状语成分，修饰主句谓语动词。

②从句中某些成分的省略现象及其结果。

一、不带连词，可以是形容词短语和名词短语——这实际为状语，修饰主句谓语动词，不是“无动词分句”。

Your friend comes to school very upset. 你朋友来学校时心里很不安。

He went to bed cold and hungry. 他又冷又饿地上床睡了。

Long and untidy, his hair played in the breeze. 他的头发又长又乱随风飘舞着。

She went away quite a child. 她离开时还是一个小女孩。

We parted the best of friends. 我们分别时是最好的朋友。

He returned quite a different man. 他回来了，成了另外一个人。

The bird fell dead to the ground. 这只鸟摔死在地上。

He returned home damp and weary enough after his ten-mile walk. 走了十英里路才回到家里，他全身湿透，疲惫不堪。

She went away from home quite a young girl and returned a mother of three. 她离家出走的时候是个相当年轻的小女孩，而回来时却成了三个孩子的妈妈了。

He got married very young. 他很年轻就结了婚。

The hare was caught alive.  兔子被活捉了。

The dog fell down dead. 那只狗倒下死了。

二、带连词，还可以是介词短语和副词短语——这实际是从句某些成分的省略现象及其结果。从句跟主句的主语一致时，省略了主语和be动词。

Mary often helped her classmates when free. 玛丽空闲时经常帮助她的同学们。

When very young, she began to learn to play the violin. 她很小的时候，就开始学习拉小提琴。　

Unless here, you can't find this kind of plants. 除非在这里，其他地方你找不到这种植物。

I could come earlier, if necessary. 如果有必要我可以早点来。

When possible, I'll come to help. 可能的时候，我会来帮忙的。

Though a young man, he has made several inventions. 虽然还是个年轻人，他已经有好几项发明了。

He is a good man，though sometimes rather dull. 他是个好人，尽管有时相当无聊。

He opened the drawer，as if in search of something important. 他打开抽屉仿佛要找什么重要的东西。