re: HSA - Minimum balance requirement question

I am on a low deductible plan without the ability to contribute to an HSA. Between how much I racked up from an unexpected hospital visit and us planning for a baby this year, we decided to change.

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If you just arent eligible for an HSA, see about transferring that HSA to one that charges you either a lower fee or no fee (not sure if they exist if its not employer sponsored, just havent done research there).

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I guess this is what I would need to look into? What were to happen if I transferred the remaining balance to the investment account? Would the savings account just go into the negative? What would happen to the investment account, assuming they can make any changes to it...