I've had tenants come in mid-month or days before/after month-end. If it's in the middle I usually just prorate the rent for the days they will be there. If it's within a few days and the room is empty anyways I don't care about giving them a few days free, as long as they don't make a fuss for not having to pay for 2 or 3 days if they move in a little later.
I'm a pretty relaxed landlord who lives in the same house though, so my situation is often different from other landlords.
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