The failover takes place and the mirrored DB now becomes the Principal DB.
For automatic failover to happen, a witness server is needed and a connection should exist between Witness & Mirror.
Will DB mirroring and the Principal DB continue to run if it has no mirror?
Yes it will continue. But the TLog will grow at the Primary as the transactions can't be truncated until they get committed at the Mirror.
So in this scenario, there is a problem of Log file filling the disk space and DB getting unavailable.
If so, then can users make changes to the principal DB and query it as normal?
Yes then can.
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SQLBuddy