Perform the following actions to stop the RBE when closing the Forms application:
1) Create a dummy report which only does e.g. a SELECT * FROM DUAL

This report has a DESTYPE=FILE and a DESNAME to e.g. C:\TEMP\DUMMY.OUT

2) In the POST-FORMS trigger add the following code:
DECLARE
pl_id paramlist; BEGIN pl_id := Create_Parameter_List('dummy'); Add_Parameter(pl_id,'ORACLE_SHUTDOWN',TEXT_PARAMETER,'Yes'); Add_Parameter(pl_id,'PARAMFORM',TEXT_PARAMETER,'NO'); Run_product(REPORTS,'<>',SYNCHRONOUS, RUNTIME, FILESYSTEM,pl_id,NULL); END;

Explanation
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The Report Background Engine runs separatly from the Forms application and there is no direct relation between these processes. The Forms should signal the RBE that is being closed. When the Form is closed the POST-FORM triggers sends a dummy report to the RBE. Since the ORACLE_SHUTDOWN=Yes parameter is used after running the report the RBE is terminated. A small side-effect of the solution is that a small file (5Kb) is created on the file-system contaning the output of the dummy report.