To rehouse someone is to put them in a new home, often a safer or better one. A government, a council, or a charity does this after a fire, a flood, or when old buildings come down. Though actually, it is not the word for an ordinary move. You would not say “we rehoused last weekend” about choosing a new flat yourself. The word is used when some organisation is responsible for finding people somewhere to live. It is more formal than rehome, and it is about people, not pets. You will meet it in news about housing, disasters, and public plans.