Can there be a relationship if there is no trust?

Yes, a bad one.

ANSWER:

I don't think relationship would work if trust is been broken. It doesn't matter if we still care for the person that took the trust that we have, things will not be the same anymore. If you continued your relationship with this person, you will notice that you have this questions lingering your mind. You will always wonder if what this person is saying is the truth. One thing when trust is been broken, its hard to believe.