I'd like to suggest that grieving is how we experience the process of a very, very deep part of our psyches becoming familiar with a painful truth. It doesn't happen only when someone dies. For instance, people go through a very similar process when mourning the loss of a romantic relationship, or when struck with an injury or illness that takes away something they hold dear (e.g., quadriplegia). I think we even see smaller versions of it when people break a precious and sentimental object, or when they fail to get a job or into a school they had really hoped for, or even sometimes when getting rid of a piece of clothing they've had for a few years.

Worth noting that a pretty mainstream emotion research theory agrees in that it suggests that the function of sadness seems to be to disengage from goal pursuit:

What is appraisal theory? In simplest form, its essence is the claim that emotions are elicited by evaluations (appraisals) of events and situations. For example, sadness felt when a romantic relationship ends may be elicited by the appraisals that something desired has been lost, with certainty, and cannot be recovered (Roseman, 1984; see, e.g., Frijda, 1986; Oatley & Johnson-Laird, 1987; Scherer, 1993b; Smith & Lazarus, 1993; Stein & Levine, 1987) [...]

In contrast to early work that viewed emotion as disorganized and disorganizing (e.g., Young, 1961), contemporary analyses maintain that in many cases emotions are likely, at beyond chance levels, to have adaptive value in coping with the situations that elicit them (e.g., Izard, 1977; Lazarus, 1991b). For example, the behavioral passivity of sadness (which involves a diminution in approach behavior) is often an appropriate response to the death of a loved one, whereas angry protests would be a futile waste of energy. In contrast, the protest and attack behavior that is characteristic of anger seems an appropriate response to physical or psychological harm inflicted by another person (insofar as it can alter the harm-doer's behavior or deter its recurrence), whereas passive acceptance might well perpetuate or exacerbate the injury (see, e.g., Milgram, 1974; Staub, 1989). [...]

Physically dissimilar events (such as the death of a parent and the birth of a child) may produce the same emotion (e.g., sadness) if they are appraised in similar ways (e.g., as involving a loss of something valued). An infinite number of situations can elicit the emotion because any situation that is appraised as specified will evoke the same emotion, including situations that have never before been encountered. Thus, the loss of one's first love or first cherished possession is likely to elicit sadness; and if people develop the ability to clone copies of themselves, a man who wants this capability but believes that he has lost it will feel sad. [...]

Several theorists maintain that the appraisal system has evolved to process information that predicts when particular emotional responses are likely to provide effective coping (Ellsworth & Smith, 1988a; Lazarus & Folkman, 1984; Roseman, 1984; Smith, 1991). Appraisals then guide coping by selecting the emotional responses from an organism's repertoire that are most likely to help attain important needs and goals under those conditions

For example, as discussed earlier, the typical response profile of sadness involves passivity and failure to pursue reward (Klinger, 1975; Roseman, Wiest, & Swartz, 1994; Seligman, 1975), whereas anger prototypically involves protest or attack responses (e.g., Averill, 1982; Roseman et al., 1994). In several appraisal models (e.g., Roseman, Antoniou, & Jose, 1996; Scherer, 1984a), one appraisal distinguishing sadness from anger is whether the person perceives control potential in the situation to be low versus high. This makes functional sense because if nothing can be done about a motive-inconsistent situation, then the passivity of sadness conserves resources— resources that protest or attack would waste; whereas if something can be done, then protest or attack could deter, reduce, or prevent the recurrence of another person's harmful action while passivity would result in a suboptimal adaptation (see also Perrez & Reicherts, 1992)

-- Roseman, I. J., & Smith, C. A. 2001. Appraisal theory: Overview, assumptions, varieties, controversies. In Appraisal processes in emotion: Theory, methods, research.