Can a mangaka continue another mangaka's manga?
Yes, it can. It is usually up to the publisher if they want to pursue continuing a series, depending on who owns the rights (family member tend to have a say in it as well). 

Note that for HotD, the plot creator was known to be a slow writer to begin with (2 years between vol. 6 and 7), and the manga was on hiatus for quite a while before his death (2011). While his death was the nail in the coffin, I don't think anyone really expected the series to ever be completed. The artist moved on to create Triage X, which basically was written as a replacement for HotD.

Below are some examples (though I'm sure there are more).


  Cases where the author died, and his team took over:
  Crayon Shin-chan
  
  Cases when the author changed, even when the previous is still alive (though it is technically a new series or spin-off):
  Lupin the 3rd
  Saint Seiya
  
  Cases where the artist died, but the original author was still alive:
  Catapillar (They replaced the artist with another one)
  
  Cases where they had someone else fill in for the dead author:
  Familiar of Zero