The floor on which he lay seemed to be white, neither warm nor cold, but simply there, a flat, blank something on which to be.

on which to be为介词+which to do不定式结构。这是书面语形式，是定语从句的一种简略形式。还原为定语从句时，只需加上主语和情态动词，将to do不定式改为不带to的不定式即可。通常省略的主语在句子中，但有时不定式的逻辑主语为泛指的人们，可以用不定代词one作还原后的定语从句的主语。多数情况下，介词加which是状语，但本句由于不定式为系词，故介词+which为表语（夸克认为方位副词或介词短语为状语）。因此，on which to be还原的定语从句为：on which one would be.

a flat, blank something on which to be=平坦的、什么都没有、人可以躺在上面的地面。（这个名词短语作补充语，对主语the floor作补充说明。）

类似的例句：

I need a piece of paper on which to write a note.

=I need a piece of paper on which I will write a note. 还原的主语为句子的主语。

This is a comfortable chair on which to sit.

= This is a comfortable chair on which one can sit. 还原的主语为不定式代词one。