Way back in the olden days, folks rotated tires to even out the wear and get more milege from a set. I’ve heard of vibration problems with some radial types. My lady friend has '94 Accord, I want to swap the worn front to the rear and assured her that the tires are balanced individually and won’t make a difference where they are on the car.
Tire rotation did not go out of style, and it is still a recommended part of regular servicing for every make of car with which I am familiar. So, tire rotation is a very good idea–if it is done on a regular basis with approximately the same number of miles between rotations. Most people use a 5k mile or a 7.5k mile rotation schedule.
Problems tend to arise when rotations are not done on a regular basis and a rotation that is very much delayed is not usually a good idea. Tire that have already acquired a specific wear pattern from being in the same position for too many miles will likely produce lots of noise in a new position.
And then, we have another problem that is potentially even more serious. Your plan–to put the badly worn tires on the rear–runs counter to the policy of all major tire makers. As any competent tire shop can tell you, the best tires are supposed to be mounted on the rear. Doing it as you plan to do will result in poor traction in wet conditions and can lead to dangerous handling qualities.
The best bet is to start fresh with a new set of 4 tires, to have the car’s alignment adjusted, and to rotate the new tires every 5k miles. If this is done, your friend will never be in the position of having some tires that are more badly worn than the others. This is the plan that I have always used with my cars, and I can assure you that all 4 tires look exactly identical in terms of tread wear.
I agree with VDC that there is no safe option involving just two tires. Starting with four fresh and rotating them often is preferred. Unequal tire wear on different axles is as bad as different tread designs. Consider a worn tire actually has better traction on dry pavement, and an emergency turn with better tread on back is already compromised in those conditions. Race drivers know balanced traction is the safest way to go and the rest of us should follow suit.