There have been people in my life that I've loved but not trusted. That may be not trusting someone's judgment, not trusting that they will make judgments that are based on reason rather than emotion (or based on reason, rather than based on what they imagine when they "put two and two together"), or not trusting someone not to do something behind my back (even if they mean well but just think they have knowledge/right to get involved with what's my business; but also if they're out-and-out aiming to be deceitful), or else not trusting them to be generally honest in the things they say. In general, these are people I've been in a romantic relationship with, though. I would not stay in a romantic relationship in which I didn't trust the person, but staying and loving/caring about are two different things.
I know people who make no secret of the fact that the way they generally operate is to feel free to whip a lie off the top of their head, just to get out of one situation or another.
So, for all these reasons, there's quite a collection of people I've known (and loved/cared a lot about) that I don't trust entirely (although some I trust at least enough to know they wouldn't intentionally do anything hurtful). But, as someone else here suggested, we can kind of work around the fact that we love, but don't entirely trust, some people; and we can know where to draw the line on when/whether we'll trust them on one issue or another.
Having said that, there are things people in all kinds of relationships can do that will betray our trust and eventually erode away at how much we love, admire and/or respect them. Romantic relationships have their own additional, and different, set of "rules"; and I think genuine and complete trust is required in them - plain and simple. But, "eroding" love and completely destroying all of it can be two different things (at least for awhile), so I can see why someone would still feel a "damaged love" that was, nonetheless, still love. :/