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I don't know much about Clifford. Virginia tells me that Sandy is taking him home to bottle feed; perhaps tease him into feeding himself. Since his past is a mystery, I'll offer an educated guess.
Clifford is the lone surviving heir to the throne of a small country inhabited only by cats. He doesn't know this, in the way of all orphaned royalty. Only after growing into adulthood and having many adventures will he one day discover his heritage.
Of course, the revelation will be anticlimatic, and redundant, since cats consider themselves royalty to begin with.