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If it rains tomorrow, come pick me up.
Literal
Tomorrow rain [subject-が] fall-[if-たら] pick-up [purposive-に] come.
A casual request. The ~たら conditional covers 'if/when,' and here expresses a conditional request dependent on future weather. 迎えに来る 'come to pick (someone) up' uses the verb-stem + に + 来る pattern for purpose-of-coming — the same structure as 買いに来る 'come to buy.' The te-form 来て as a standalone sentence-ender is a casual imperative/request form ('come, please'), dropping the ください that would make it more polite.