The first thing I would look for is a crankcase vacuum leak: at the
valve cover, air intake hoses, oil intake cap, etc. The EGR valve could
be clogged, or the EGR vacuum solenoid could be bad. The VSV (vacuum
switch valve) could be bad. See:
http://www.autoshop101.com/forms/h61.pdf

Exhaust gasses recirculate into the valve lifter chamber / crank case
to be reburned, to cut down on oxidated nitrogen and carbon that would
otherwise be ejected from the tailpipe; when under acceleration, the
high RPM creates a high vaccum in the system that must be regulated or
the vacuum would suck too hard---- that regulation involves opening the
system to intake a large volume of exhaust gasses. When slowing down
and coming to a stop, the vacuum controls pinch off the exhaust gas
intake. If there is a break in the vacuum system (hose came off, or is
punctured), atmosphere gets sucked into the exhaust recirculation
system that the controls cannot shut off: the vacuum cannot be made
high enough to keep the engine's RPM high enough to idle properly.

Then again it could be something totally different. It could be as
simple as adjusting the engine's idle.

My pickup stalls when coming to a stop and when the engine is hot: I
suspected the positive crankcase ventalation valve (PCV valve) is stuck
open, but now I think it is due to the huge hole in the air intake hose
that I found three days ago.

I'd pop out the MAF and give it a good cleaning with some contact cleaner
(available at Radio Shack, etc.) -- mis-read airflow can cause all kinds of
issues.   Cleaning the throttle body would also be a good  idea, and easy to do.