This is not truly a situation involving a 'hit and run", or at least it is a variant on that theme. Perhaps this situation can be though of as a 'delayed hit and run'. In other words, the person responsible for the accident stays at the scene, but later disappears, at least for all intents and purposes.
The law describes this as as situation wherein the identify of an at fault driver is known, but they cannot be served with process for a court case, and it is unknown whether their car was insured.
It has been suggested by scholars that such a claim should be a cognizable uninsured motorist claim [Andrew Jancitto, Maryland Motor Vehicle Insurance, 2d, 1999].