Lisa, it's possible to omit "who" in this sentence:
The man I wanted to meet got sick. <grammatical>
Below, "who" functions as a subject. It's the subject of "lives" and "has",
The man who lives next door has a good sense of humour.
I want a man who has a good sense of humour.
In short, it's not possible to omit a relative pronoun if it functions as a subject.
Hope that helps.