It would not be uncommon for an intermittent crank sensor failure to cause a stalling condition for your 2001 Cadillac DeVille DTS. The first step would be to scan the Powertrain Control Module for fault codes. Any stored codes should be diagnosed and repaired as necessary.
I have a 2003 and was told it was my upper crankshaft position sensor when my car would just cut off but start back up and do the same thing maybe two to ten days later, always starting back up.I had it diagnosed and a code PO335 and 338 showed up so I'm having the upper and lower replaced ASAP. I hope that does it. Have a check done on the engine.