At some point you will need to formally dissolve the entity, otherwise you will still be charged the annual state tax in Delaware. It's not clear whether you formally qualified the LLC to do business in Virginia, so I can't comment on your obligations in Virginia.
Delaware requires the payment of the franchise tax each year regardless of whether the LLC earns income. In order to comply with the law, you would be required to pay back franchise taxes (together with late fees, interest, etc.). To avoid incurring future franchise taxes you would be legally required to formally dissolve the LLC. See generally 6 Del. C. s 1107.
Failure to pay franchise tax for three years causes the LLC to automatically dissolve by operation of law. 6 Del. C. s 1108. This is what you mean by letting it "go void".
Franchise tax due and owing is considered a debt of the company, and the state has various powers available to it in collecting its due. See 6 Del. C. 1107(g)-(j).
The power of the state to collect past-due franchise tax from the personal assets of a member or manager, however, is strictly limited under 6 Del. C. 1107(n). It's possible depending on the circumstances that the State could attempt to collect past-due franchise taxes from a member, and the chances of this happening and/or being successful depend on a large number of factors that can't be addressed here. I have never heard of this happening in Delaware (it does routinely happen in some other states, like California).
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