Solder various parts of broken wire in a fan coil
There will not be enough slack to get the proper broken ends to overlap each other and twist them together to get enough of a mechanical connection for the solder to hold them together. You would need to have some additional wire of the same size to overlap the gaps. You would need to remove the insulating varnish from the areas that need to be soldered.
As mentioned in another answer, you need to connect the wires as they were originally. Each broken end must be reconnected to the end it has broken from. If you get them mixed up, part of the coils will be bypassed. I would not be confident that you can determine what goes where with a multimeter.
Getting the wires re-insulated will be challenging. The wire must not &quot;touch on itself.&quot; That would bypass some turns of the coil. Depending on where that happens, the fan could get hot and burn immediately or sometime later.
This might be a good challenge to learn from, but it you are successful, I would still not consider it safe the leave the fan running when you are not watching it. Give it a try, but buy a new fan and throw the old one away regardless of the outcome.