"sense of closure," usually refers to a psychological need to have a problem, usually a painful problem resolved in some way. The use of the word fulfilling is a bit redundant beause the "sense of closure" fulfills a need.

HERE ARE SOME DICTIONARY REFERENCES:


4. closure - something settled or resolved; the outcome of decision making; "they finally reached a settlement with the union"; "they never did achieve a final resolution of their differences"; "he needed to grieve before he could achieve a sense of closure"
http://www.thefreedictionary.com/closure

closure (definition)
5. Chiefly US
a. the resolution of a significant event or relationship in a person's life
b. a sense of contentment experienced after such a resolution
Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003
(from website above also)



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Note added at 2 hrs (2010-07-06 12:31:57 GMT)
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HERE'S A DISCUSSION FROM HARVARD UNIVERSITY about sense of closure, or how to conclude a written piece of work:

So much is at stake in writing a conclusion. This is, after all, your last chance to persuade your readers to your point of view, to impress yourself upon them as a writer and thinker. And the impression you create in your conclusion will shape the impression that stays with your readers after they've finished the essay.

The end of an essay should therefore convey a sense of completeness and closure as well as a sense of the lingering possibilities of the topic, its larger meaning, its implications: the final paragraph should close the discussion without closing it off.

To establish a sense of closure, you might do one or more of the following:


Conclude by linking the last paragraph to the first, perhaps by reiterating a word or phrase you used at the beginning.

Conclude with a sentence composed mainly of one-syllable words. Simple language can help create an effect of understated drama.

Conclude with a sentence that's compound or parallel in structure; such sentences can establish a sense of balance or order that may feel just right at the end of a complex discussion.

http://www.fas.harvard.edu/~wricntr/documents/Conclusions.ht...