Most verbs use either avoir or être as the auxiliary verb in Le Passé Composé (Indicatif) (or other compound tense), but demeurer uses both, depending on its grammatical usage* and what it means in the sentence.
Using avoir or être with the verb DEMEURER in Le Passé Composé (Indicatif) in French
être + demeuré + [adjectif]
= to remain + [adjective]
When demeurer means to remain in a state of being it takes être.
ATTENTION:
Do not confuse demeurer with être in Le Passé Composé (Indicatif), and the very rude expression être demeuré/e which means to be stupid (and like I said, very offensive). The main distinction is that in the second case, demeuré is the adjective, therefore there won't be another adjective afterwards.
avoir + demeuré [quelque part]
= to live [somewhere]
= to stay [somewhere]
When demeurer means to remain or live somewhere, it takes avoir.
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