if above occurs should i have to pay for the new coil?
Depends. How old is the car and why did the coil break? If they were throwing hammers at each other and your car was in the way then it is their fault. In reality usually it is always a case of “it was bound to break” and then it broke there. For most cases if you pay for the part but not the labor it is fair to both parties, esp if you are otherwise happy with your mech. Mistakes happen too.
All I can say is IF he broke it he should fix it. I have had things break in my shop and I always fix them on my dime.
What kind of Toyota is it? $160.00 seems like a lot for a coil. Didn’t he give it to you at cost?
That’s a coin flip IMHO. I assume this is a coil on plug setup?
If so, and if the coil has been on there since the dawn of man, then it’s always quite possible the rubber and plastic has hardened due to age and heat.
On removal, things can break.
You may see the same thing if a thermostat housing has been in place for many years. Often the 2 mounting bolts will corrode into place and may break off during removal. It’s no one’s fault; just the way things are in the mechanic field.
The same is true with water pump bolts, wire connectors, or spark plug holes stripping out due to the spark plugs being left in place for so long. JMHO
Does the latter have anything to do with this broken coil?