I'm hoping to gain an understanding of what happened locally in a province as it left the empire. Some questions that came to mind were as follows, but I'd be interested anything I might have missed as well.
Was a loss of territory usually preceded by a revolt, or did some other factor trigger this loss? Did many Romans stay behind, or did most return to the empire? Was any form of government installed when they left or was there a free for all to secure control of the area? Was any of the Roman infrastructure actively maintained once the province was independent?
This answer by u/Iguana_on_a_stick does an excellent job of covering most of what you're talking about, but to add in response to one of your other questions:
Was a loss of territory usually preceded by a revolt, or did some other factor trigger this loss?
The exact details of what happened were different for each province. Broadly however, we can consider a province 'lost' when it's no longer under direct central control, which in practise means when there is no longer an army to defend it. In the case of Britain, the army 'rebelled' in 406, creating and murdering two emperors in quick succession before they settled on another general, Constantine III. He led the troops out of Britain to Gaul in 407, and thence to Italy where, after various shenanigans, he was finally executed. While Britain was still theoretically still a Roman province, under the command of the Emperor, no Roman troops would ever be sent there again, and letters sent to the Imperial court requesting help between 446 and 454 were left unanswered. A fairly similar process unfolded in the Iberian Peninsula, and subsequently in North Africa: troops left the area, and within a decade or so practical authority was being exercised on a local basis.