Hypothetically, if neutrinos lost their energy in the expanding universe, slowed down, and collapsed in a vast and otherwise empty region under their own gravity, they might form a large object usually referred to as "neutrino star". The Pauli exclusion principle would not allow neutrinos to collapse all the way to the center, so they would form a surface that with enough gravity might be liquid or solid.
My question is on the Pauli exclusion principle. Would it allow me to stand on the solid surface or sail in a boat on a liquid surface of a neutrino star? Or would I just fall through all the way to the center, because I am not made of neutrinos and the Pauli exclusion principle for neutrinos does not apply to me? If so, what would be my experience? Would I feel the presence of the dense neutrino matter or would I perceive this star as a gravitational trap in a seemingly empty space?