Ernie,
I agree with Jeff, it doesn't seem likely that the clutch slave is related to engine dying at idle. It should idle in neutral with clutch engaged just fine, there is almost no load on the engine in that situation. My car (manual trans) had similar symptoms for a while; idled fine some times, idled rough and died other times. I retuned it about 3 times, and raised the idle speed a bit. This helped but didn't quite cure it. I then adjusted the vacuum unit in the distibutor to retard timing about 1 degree at idle, then retuned at idle (about 850 rpm), and it no longer dies. I can't really explain why this worked, but it worked. No parts replacement at all, just making those adjustments. In your case, I'd suggest a careful retuning at idle and maybe raising the idle speed a bit first, that may be all it takes.
Good luck!
George Davis
'69 280 SL Euro manual