structure of "alternative to people sleeping on the streets"

Question

Consider this sentence

There must be an alternative to people sleeping on the streets.

I understand the first half "there must be an alternative", a simple there be + sb./sth.

I also understand the use alternative to + sb./sth.

I don't understand the structure of the remaining part. I guess the whole part "people sleeping on the streets" could be called reduced relative clause, and "sleeping on the streets" functions an adjective that describes people. However, directly convert the present participle to a relative clause does not seem to work.

There must be an alternative to people who are sleeping on the streets.

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Note: I understand the meaning of the sentence, I just don't understand the structure.

Answer 1

"People sleeping on the street" is a gerund clause. It is a clause with the verb in its participle form "sleeping", functioning as a noun.

You could say, for example

Pears are an alternative to apples.

You can see the word "apples" is a noun. By analogy to this, the phrase "people sleeping on the street" is a noun phrase, and this one is a gerund.

Answer 2

"People sleeping on the streets" means there are homeless people. Saying "there must be an alternative" means that the writer finds the societal condition of homelessness unacceptable, and insists that there must be an alternative: a solution to the problem of homelessness.

"People sleeping on the streets" can be analyzed as this relative clause: "People who are sleeping on the streets" reduced by removing the relative pronoun.