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If you have agreed with the landlord to pay him rent, and you haven't done so, then he can pursue you for breach of contract for any amounts that the security deposit doesn't cover. The fact that you are voluntarily moving out wouldn't somehow erase the debt that has accrued unless you get something in writing from the landlord stating that he is wiping the slate clean.
But if your security deposit covers any delinquent rent, damages, and cleaning costs, then he wouldn't be able to pursue you for anything else.