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