Yes. Context will normally make the difference in meaning clear.
Despite what many people who ask questions here seem to believe (I am not referring to you, navi) one sentence on its own often gives insufficient context for us to be able to say that only one interpretation is possible. Before anybody writes in to say that meaning #a would be clearer if 'whenever' had been used instead of 'when', or 'used to go' instead of 'went', I'll just say that it would - but the meaning you suggested is possible with the original words.
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