Well, this is a very complex question...and a serious one.
Short answer 'yes' trust can be built up.
Not knowing why? it has been broken, is also hard to answer.
If it has been badly broken by something serious, then she must work out 3 things.
1.Does she love him still.
2.Does he love her still.
3.Is she willing to move forward, believing he will not do it again.(what ever it is).
If it is yes to those questions, it can be fixed.
Some people have had it happen, and have become even stronger than before...Because they were really in love.
Forgiving is part of life, and we all fall short in one way or another.
Some find out, others don't.
Finding out is a very good thing, now one has to ask''do I want to help mend this mess'.
Time as with anything, has to be your 'key-player' in this.
Once one has made the choice to stay with it, and learn to trust again...You can never ever bring it up again.(What the other has done).
It has to be put to death, never to raise it's ugly head again.
That is the hard part, forgiveness, has to be that.It must not be spoken about again.
That's where it is a 'grown ups' world. Success, is founded in strength.
From both parties.
The one who has done wrong can not be punished over and over, they will have to live with the memories for the rest of their lives, of what they did anyway.
We often think, ''oh they will forget''.They never do.It is impossible to forget.
So the one who has been wronged, in the big picture comes off better in a case like this.They do not have the guilt.
It is something the two of them need to sit down, and work out.No one else can really know, what they can do or want to do.
It is achievable,but hard work and lots of love for both, and time.