I am not familiar with Blackbaud, but if the status of the student changes from "enrolled" to "dropped" (or whatever status terms are used in Blackbaud), then your SIS import file should reflect the change of state.
When a student enrolls in a course, you send the SIS student import record with a status of "active"
When a student drops a course you send the SIS student import record with a status of "deleted"
Take a look at the possible status values defined in this document:
SIS Import Format Documentation - Canvas LMS REST API Documentation
Scroll down to the definition of the "enrollments.csv"
The definition of the "status" field shows the following values: active, deleted, completed, inactive
It is up to your systems integrator to craft the querries against the Blackbaud database that will recognize these changes of status and create the SIS enrollment import file properly reflect these values. By sending the appropriate status Canvas will automatically update the roster to represent both student adds and student drops.
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