A fragment, in some cases, can refer to an aspect of a personality that has not yet developed, and may never develop, into a full identity - but nonethess displays traits seperate from other personalities and can often act independently.
Most commonly, a fragment will either dissipate, or develop on its own into a well rounded identity.
Fragments, in some instances, can arise when a person unknowingly sperates traits that they are scared of, or find 'bad' in some way, away from their core ego. Whether a singlet or a multiple, the fragment will inhabit the back corners of the mind. Usually these are more shallow shadows of personality -anger, lust, even confidence or assertiveness. Fragments are often classified as 'evil' by the rest of the mind(s) for this reason.
Often, the fragment will develop on its own, or make a concious choice to become an identity. When this happens, the fragmented traits will latch onto the conscience of the individual, and a true seperate identity will develop, with his/her own individual style.
An 'evil' fragment may become a wise friend, or a sullen snob - but rarely does the resulting identity that grows from the fragment of personality have true evil intent.