Interference engine

My car's timing belt and water pump broke
the other day. I was going at a very slow
speed when my car just shut off and no
longer worked. We took it to the shop and
he said that I had an interference engine
and it's possible that my engine is totally
shot after this. But I was wondering if
because I was going a slow enough speed
that the pistons probably didn't damage.
However my mother did try to start the car
multiple times (I regret calling her may I
add) and I don't know if that would actually
cause any damage regardless of how slow I
was going.