If & only if you're using LW 4.12 can you resume them from where they were. If your system crashes or some other reason that caused it, going to the Library window, selecting incomplete files & pressing Resume will force them back into the download window. If they start downlding they will resume from where they were. But may show zero % until they do start downlding again.

However, in earlier versions of LW they would always start from zero % after resuming.