Overview
Over Budget Permissions setup defines and controls budget check behaviour in the event that insufficient budget funds are available.
The setup defines what permissions are granted to users that are members of specified user groups
Prevent processing at over budget threshold and Prevent over budget processing will stop a user from being able to further process the transaction that is subject to budget checking e.g. purchase order, in the event that either the remaining budget available exceeds the budget threshold specified in budget control parameters, or on the applicable budget control rule … or the value of the transaction being checked is greater than the remaining budget funds available.
Allow over budget processing will continue to allow the transaction that is subject to budget checking to be processed in the event that there are insufficient budget funds available.

Further Reading
Further information on Dynamics 365 Basic Budgeting and Budget Control is available on the Microsoft Docs and Learn Docs sites via the URLs below and should help to provide further background and context to aid survey question completion.
Budget control overview – Finance | Dynamics 365 | Microsoft Docs
Public Sector
Background and information on the Public Sector specific elements of Basic Budgeting and Budget Control are provided via the URLs below for reference purposes.
Set up budgeting and budget control for apportionments (Public sector) | Microsoft Docs
Set up budgeting and budget control for a preliminary budget (Public sector) | Microsoft Docs