Look for a hole in the PCV valve hose on the backside of the engine.
A faulty muffler will not cause this but a clogged catalytic converter will.
There are multiple things that could cause this, your best bet it to take it to a mechanic and let them check it out.
look to see if your intake manifold is gummed up with residue
A bad fuel pump will cause your vehicle to not start or sputter and then stall. A dirty air filter can have the same symptoms.
Could be a fuel pump going bad or a clogged fuel filter,
They start to sputter,stall and stop running.
Lots of things. From misfiring spark plugs to incorrect timing to deposit build up.
Start with replacing the fuel filter, it may be plugged.
coz you shud of gone to specsavers
FUEL PUMP IS YOUR PROBLEM {why do you think its the fuel pump?}
it may be the maf sensor i got a corolla 2001 too do you have any codes ?this is a old question thought.
A clogged fuel filter or fuel line will likely make your car sputter as if it is going to stall.