Due to a slowdown in business, several employees had their hours reduced to the point that they are no longer eligible to participate in the medical benefits program.  They are still employed on a PT basis, AND are eligible for COBRA. 

The conditions under which they lost regular coverage was involuntary, so do they qualify for the subsidized premium payment?

Reduction in hours doesn’t count as “involuntary termination” and it doesn’t make an employee eligible for the subisidy.  They have to be separated completely.