In the Nonprofit Success Pack (NPSP), Salesforce implements strict data integrity guardrails to prevent the accidental loss of financial history. One of the most critical protections involves the deletion of Account records that have associated "financial" records.

According to NPSP documentation and standard database behavior:

Opportunity Protection: An Account cannot be deleted if it has any associated Opportunity (Donation) records that are in a "Closed/Won" stage. This is a hard-coded safety feature in NPSP's trigger framework.

The Error Message: When a user attempts to delete the Household Account, the system will halt the operation and display an error message such as: "This Account has Opportunities. You must delete all Opportunities before you can delete this Account."

Audit Integrity: This ensures that the organization's total revenue figures remain accurate. If a household gave $1,000 last year, deleting that account would "orphan" or delete those gifts, leading to a reconciliation nightmare in the general ledger.

Regarding other objects:

Affiliations and Relationships (Option C): These are child records of the Contact, not the Account. If you were deleting a Contact, these might be impacted, but they do not typically prevent the deletion of the parent Account directly; the primary blocker is the financial transaction.

Option A and B: These are incorrect because they imply the operation would either complete silently or be ignored without feedback. Salesforce always provides a clear error when a trigger validation (like NPSP's Opportunity check) fails.

To successfully delete such an account, the admin would first have to delete (or re-parent) the Closed/Won Opportunities.