1997 Suzuki Sidekick Keeps dying when I slow down

Maintenance/Repairs
1

Every time I go to slow down- This car has a manual tranny and when I down shift to a lower gear when approaching a stoplight or stop sign the RPMS drop to 0 and the car dies. I have been catching it by putting the car in neutral and pushing the gas pedal, however this is tricky in certain situations(a hill). Strangely enough, after I give it the gas I can then put the car in neutral and it is will not die. But if I don’t catch it in time the rpms drop to 0 and shuts my car off. any suggestions? Thank you