I think Julie hit the nail on the head: the status of the couple's relationship is their business, and they'll need to work it out.
Absolutely do not talk to her boyfriend, or they will both likely be very upset with you. This is something you will have to be stoic about, because I see you obviously care about your cousin's feelings, but getting involved beyond listening and empathy is to run the risk of alienating them both.
What might be a safer suggestion: if your cousin is upset enough about this to want some peace, she might go to see a counselor. I'm a person who has been both married and also in a long-term commited relationship for years with a person before marrying them. Both situations worked for me for what I needed; when it stopped working, those situations changed --one declined, one improved, so you never can know. Doing the work to figure out why we are in the situation we are in can be helpful; sometimes we decide that we're okay where we are, and sometimes we make other choices.
We can love someone to pieces, but we have to love our own selves first. Ultimately, your cousin must decide how she wants to live--and doing this can sometimes look like a long process (Don't expect her to make any lasting decisions overnight, if she does decide to address it.) In my opinion, there's nothing *wrong* with either situation if it works for her values and is meeting her needs. If not, change is good.
H.