Sure, I think there's a parallel, particularly if you consider that a person is not an isolated, self-contained entity, but rather a being-in-relation. Your identity is defined partly by your relationships with particular others, and the more intimate the relationship, the more it contributes to your identity. Intimacy is a matter of sharing first-person perspectives (what the world looks like from your eyes is shared with your intimate, and what the world looks like from hers is shared with you) as well as plans, goals, projects, etc. In fact, in a truly intimate relationship, you'll adopt the plans, goals, projects, etc. of your intimate as your own. When the relationship ends, especially if it is ended unilaterally, all of this that had been part of you is to some extent alienated, which would suggest that your identity is changed. The person you were, in intimate relation with that particular other, doesn't exist anymore. So it is, in an analogous sense, a death. But it's not as complete...

Like many terms, there is a variety of definitions, and which is most appropriate would depend on the function or context of its use. A classical definition of death is "separation of the soul from the body." But to someone who denies the existence of an immaterial soul, it would probably be something more like, "Cessation of bodily processes, including those on the cellular level." More fundamentally, death would be the absence of life where there once was life. But then, of course, you'd need a definition of life. Philosophy has always been concerned with proposing, criticizing and defending definitions (as opposed to asserting them), so these should be taken as opening round suggestions.