Yup, so if your Resilience drops to 0, any additional damage gets applied to your STR and then you need to make a Critical Damage save (a STR save). If you pass this, you live. If you fail, you die.
All subsequent damage lowers your STR score directly and causes another Critical Damage save. If you fail any Critical Damage saves or if your STR hits 0, you die.
The same applies to monsters and NPCs as well. The goal is to reduce your opponent’s resilience until you can start reducing their strength.