Catch 22 in healthcare

What would you do if you are a PI and your graduate student/postdoc gets really sick (over a few months) and there is no alternate funding than say the NSF or NIH grant?

On one hand:
You are responsible for work to be done in a timely manner to said agency, and cannot pay someone who is not working.

On the other hand:
The way health care works here no job means no health care... when the grad student/postdoc needs it. Let alone that the person's dependents would loose healthcare as well if they are on the same policy.

Furthermore:
if the person is foreign, do they get expatriated.

I am sure similar stuff comes up when faculty and staff are reviewed.

It just seems inhumane. I wonder how these would ever be handled without some kind of universal health care that is not dependent on work.

I am reminded of this over these holidays by randomly trying to get information from the registrar's office at my Ph.D. school. In that department, one of the first years (so not even on a grant but on TA) got sick. He was American so no foreign rules do apply. He tried to get home and passed away. The questions I never learned the answer to is
1) why was he allowed to drive home instead of being in the hospital.
2) would it have made a difference if he was on the RA insurance which was better than the TA insurance
3) would they have extended his TA ship so he will continue to have healthcare had he not passed away during break.

On other news my test for potentially very harmful disease came back... Negative. Big sigh of relief.