You are way out on this one Colin and LB - perhaps as we are local we get more of the story on the news than you do.
The family were here on the wifes visa as she was working as a nurse in the same hospital that she was to die in.
While giving birth in that hospital she was administered a drug which is meant to be given only as an epidural into the spine but instead was injected into her arm killing her.
This has to be negligence and the hospital have not even apologised for their mistake.
This family has lost a wife and mother and because she is now dead (there was no reason before, as she had a visa) have come under the deportation spotlight - if any family (what is left of it) have a right to stay and see justice done - they do.
You can not put them in the same category as the vast majority of cases that exist i.e. terrorists, thieves and general spongers.