You<em> can</em> use 'that' here. It is a valid alternative.

Whoever downvoted my comment about 'that' being a valid alternative might like to consult their grammar book. Here is an explanation:

The phrase "all the people who were asleep" contains a <em>defining relative clause</em>. In defining relative clauses, both 'who' and 'that' can be used to refer to people. It is perfectly correct to say "all the people that were asleep".

It is only in <em>non-defining relative clauses </em>that we are restricted to the relative pronoun 'who' for people. For example:

"The people, who were all asleep, were unaware that the building was shaking."

In this sentence, the clause 'who were all asleep' provides additional information about the people, but does not define them. The clause has to be between commas and the pronoun has to be 'who'. You cannot use 'that' in this clause. However, you <em>can </em>use 'that' in Darcy's original sentence. Anyone who doesn't have a grammar book handy and still doesn't believe me can just do a search for 'relative pronouns'. It's all there in black and white. Or even in colour, if you're really lucky.

Upvote for Su.Ki's comment.  Downvote for Alaa because she was wrong, but she did say "I think" so no harm done.

If anyone wants an online supporting reference to Su.Ki's explanation, here is one. https://owl.english.purdue.edu/owl/resource/645/01/  

If anyone disagrees with Su.Ki, myself and Purdue University, I think it would be reasonable to post your reasons openly so that we can all have a discussion.  Perhaps then you could consider downvoting if you are still not happy.

The only thing wrong with this sentence is that there is a word missing before 'building' ('the' or 'our' or another determiner is needed).

i think "that" refers to things not humans or persons