I don't see it that way. It's not implying the kids are dead, or any sock puppet speculation or admission of death - it will be the state witnesses' testimony that the status of the children is not known, and I would expect that would have to be an established fact to determine a failing of duty of care.
LV need only commit the actus reus of the offence at some point in the past.
There is plenty of evidence that can be placed before the Court to support the obvious and natural inference that she has abandoned the kids and failed to support them. Namely they have not been in her custody for months and she has not made any financial provision for them.
I agree the prosecution cannot prove the kids current status, but for these proceedings they don't need to.
Of course the defence can try to speculate some exculpatory version, (e.g the kids are in hiding) but without hard evidence to support such a contention, it is hard to believe it would be successful to raise a real doubt.
Of course it is always possible to imagine an exculpatory version (eg the kids died in an accident so weren't abandoned) but I think that is too theoretical. The defence would have to place a definitive version on the table rather than merely suggesting things within their direct knowledge might of happened or can't be ruled out
Any jury properly directed, is entitled to make the obvious inference
Otherwise it would be possible for LV to defend these charges by implying she might have murdered the kids. IMO that is an absurd result that for practical reasons, cannot succeed at trial.