No the cells might become contaminated with the other cell line, you don't know what you are actually treating your cells with. You should use fresh reagents.
When the cells died, they might release a lot of different toxic substances. I agree with the other comment that in this case you do not really know what you will put on the other cells. Whether you can in principle re-use your transduction medium depends on the type of viral constructs you have. If it is self-inactivating you can't use it. If it is not, you could re-use it, but in this case just discarding it is very dangerous.