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It depends on the situation, I think. Everything depends.

I will fight for my love ones if I know that his/her new ones isn't okay, but I will let him/her go if she's happy on her decision.

It is a way of saying that your love for him/her is true and likewise stating that you will have no say in what other people thinks about your relationship. no matter the odds you're always and forever will pick him/her anything.
but when a person sees that his/her partner is unhappy, don't fight just let them go, they will eventually find their way back if you two truly belong.