Does Process Builder run with System permissions or User permissions?

According to this answer:

Process Builder runs in the system mode so the object and field level permissions both will be ignored for the user who triggers the Process.

Process Builder always runs in System context and hence you can edit the record or read the record even if user does not have access to the same .

1. System mode: – In which the object and field-level permissions of the current user are ignored.
2. User mode: – In which the permissions, field-level security, and sharing rules of the current user are enforced.
3. Flow runs in user mode.
4. Process Builder runs in system mode. When you launch a Flow using the Process Builder, then it will run in system mode.