Underwater Foreclosure If Payments are Up to Date

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Can a lender typically foreclose on a single mortgage property when it goes underwater, if the payments are kept up to date? In this example, lets say the mortgage is for $500K and the property was $700K and is now worth $350K.

Are there typically terms in the mortgage that prevent or allow this?

Are there differences by state?

I'm just trying to understand the general situation, not looking for legal advice or an answer in a specific situation at this point. - standard disclaimers about questions apply.

Thanks very much.

sw