Saw this in the news:

"Virgin birth has scientists buzzing: Researchers discover a gene in honey bees that causes virgin birth." 

The title of the actual study is a little less sexy:

"A Single Gene Causes Thelytokous Parthenogenesis, the Defining Feature of the Cape Honeybee Apis mellifera capensis"

essential point:
> Thelytokous parthenogenesis differs from arrhenotokous parthenogenesis because of an unusual orientation of the meiotic spindle after meiosis II that results in the fusion of the two central pronuclei. 

As Ruttner (1983) explains:
 >The most conspicuous characteristic of the [Cape] race is the faculty of worker bees to reproduce by thelytokous parthenogenesis. Due to this phenomenon, a queenless and broodless colony of Cape bees, in any other race destined to perish, is capable of self-preservation. A queen may be reared from parthenogenetically produced female larvae, which will take over the colony after mating.  TUCKER (1958), suggested that automictic workers are derived from the union of two haploid nuclei, formed by complete meiosis.

comments:

In other words, the paired chromosomes of the eggs segregate in meiosis, in order to be able to join with the (unpaired) chromosomes of the sperms, thereby producing a diploid offspring (paired chromosomes) which are normally females. In the case of the Cape bee, the unpaired chromosomes join with others (no sperm needed) restoring the paired state of a normal female. 

The drones are haploid, having unpaired  chromosomes. (This does not address the issue of diploid drones, which don't survive anyway.) This type of reproduction is called automixis. It does not come into play with the production of drones, since the have only one set of (unpaired) chromosome. Both queens & workers can produce these at will. 

diploid = having a full set of paired chromosomes
haploid = having one set of single chromosomes (aka.  monoploid)
polyploid = having multiple copies of chromosomes (polyploidy is common in plants)

> In mammals and birds, ploidy changes are typically fatal, with polyploids dying early during development. Example: triploid XXX humans, which develop as females. Evidence suggests that a general disruption of development—not problems restricted to sex determination—is the root cause of the failure of polyploids to persist. --  Otto, Sarah P. (2007). "The Evolutionary Consequences of Polyploidy". Cell. 131 (3): 452–462.

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