I'm sorry to hear about what happened to your mother. It's good that the other party has reached out to you and is willing to provide compensation. However, it is important to consider a few things in this scenario:
1. Legal implications: Accepting the 10k offer without involving the police may have legal implications. It's important to consult with a legal professional to understand your rights and options in this situation.
2. Safety concerns: If the other party is hesitant to involve the police due to fear, it's important to prioritize safety for both parties. You can consider meeting in a public place or having a third party present during the discussion.
3. Evidence collection: Even if there was no evidence at the scene, it's important to gather as much information as possible now. This includes details about the other party, their vehicle, and any witnesses to the incident.
4. Closure and justice: While accepting the compensation may provide some closure, it's essential to ensure that justice is served for your mother. This may involve reporting the incident to the authorities and cooperating with any investigation.
In this situation, I would recommend seeking guidance from a legal advisor to understand the best course of action to take. Your priority should be your mother's well-being and ensuring that the responsible party is held accountable for their actions.