What would you call someone whose unmarried partner has passed away? If they were married, the word would be widow(er). Ex-partner/ex-boy/girlfriend doesn't seem to fit either because the two never broke up, except their partner is dead so they aren't technically together anymore.
There's no word with the specific meaning of a person who has lost a girlfriend or boyfriend, but you can use the word bereaved. This can be used for the loss of anyone close, including close friends and other family members.
Normally this is used when the death was relatively recent, and the person is still suffering from the loss.
"The bereaved will need the support of her friends during this difficult time."
Survivor. Source: WordWeb. Surviving partner, as Mari-Lou A says, would be a more formal version.
Colloquially, I have heard widow(er) being used for long-standing unmarried relationships just as well as for married ones. The significance of official marriage in regards to everyday language seems to have declined quite a bit.
Rather archaic (I've only ever seen it used on tombstones), but relict was also used for 'common law' widows/widowers as well as legally married ones.