Is it common to see building wire used for a doorbell?
It is not common because of cost but it’s also not uncommon. I agree with Harper if I have a broken bell wire I would use something on the truck to repair the wires. Since it was repaired you may get lucky and be able to use the existing wires as a pull. 

I would use a pull string , but you may have some stout fishing line that could work. The trick here is figuring out where the break or short is. 
At the chime disconnect the door bell button and verify you have 24v , some transformers have a bridge that converts to dc so you need to know what you are trying to measure unless your meter automatically checks for both. If there is voltage at the chime  we know the problem is probably at the splice. 

I would use the wires as a pull. I would tie a pull string to the bell wires and pull that direction because the bell wires are smaller and if it will pull small wires following a large cable will work easier than trying to pull the other way. 

If the wires are stapled and I now know I will have to open the wall sometimes I will pull to the breaking point and the splice may pull free then I would measure the length go up to that point and open the wall, it may save a lot of repair work if you can fish the new wires down the wall.

Just to clarify the string or fishing line is used to pull new wires from the button to the chime. Pulling the wires out at the button location , hopefully until the string or fishing line arrives at the button location. Standard pull string is rated at over 100 pounds.