I asked a friend who is a highly competent EE by day - but who restores super sized steam engines by night and collects olde heavy metal engines etc and has much experience with old large corroded items. His comments:
It really depends on the specific situation.
For mild steel bolts in good condition which have not been too excessively deformed, and where the nuts are in reasonable condition, it is often possible to "re-form" the damaged threads by applying sufficient torque to back the nut off. In some case you can encourage this to happen by carefully grinding the deformed end of the bolt to get it back to something close the original nominal thread diameter. You can also increase your chances if you apply a penetrating lubricant (and any lubricant is better than none). Applying heat may also help if that is possible - and if you can apply heat and then apply lubricant at a temperature where it is not broken down the lubricant will tend to be drawn into the thread as further cooling occurs.
If the nut is in poor condition or the shaft of the bolt has corroded and become "waisted" your probability of success will be pretty low. If just the nut is corroded you may be able to split the nut with chisel, but you then have the problem of how to reform the threads. If sufficient bolt end exists you may be able to use a die to cut new threads, but you will then have to use a bush under the new nut to take up the length of the remaining old thread as the new thread is unlikely to run into the old properly.
In some cases you may be able to reduce the diameter of the bolt and cut a new thread at the reduced diameter. If you are willing to make you own nut, you have full freedom as to the diameter you choose - at the expense of a non-standard thread for your successors to deal with when its their turn.
For high tensile bolts your job is much harder and I think the chance of success pretty low - and you will probably need more specialised equipment. A carbide shell type cutter which fits over the bolt thread may allow the nut to be cut away and perhaps a die grinder could be used to clean up the thread so it can be re-cut (but even HSS dies will struggle with high tensile steel).
There are special repair kits available that work a bit like concrete anchors. They have a nut with a segmented sleeve which has sawtooth ridges on the inside and is slightly tapered. You slip it over the (suitably prepared) bolt end and then tighten the nut. As the nut tightens it compresses the sleeve which in turn bites into the bolt. Don't ask me what they are called or who makes them.
There is also some process used in civil engineering that allows a failed steel tie in a blind hole to be repaired in-situ. It must be some kind of welding process but I have no idea how it might work. I believe that it was used to do some repair work on the bridge over the Grafton gully [in Auckland, New Zealand]. I think it is also be used to extend existing concrete bridge structures when the roadway underneath the bridge must be widened.
Source: Ken Mardle.