It depends on the species, we have Fagesia spec. (about 3m high) it is clumping not running. One of them is contained by a root barrier 1m deep, it stayed there

It depends on the species, we have Fagesia spec. (about 3m high) it is clumping not running. One of them is contained by a root barrier 1m deep, it stayed there for now 13 years, the other on is planted without a barrier and after 8 years it started "invading" the lawn - but very very slowly (about 20cm) - you just could use a spade to remove it every other year. The barrier was just a very thick and stiff synthetic canvas.