It will still focus, but it depends upon which position the switch was in when it broke off. If it's on the "Limit" setting, it's going to be quite limited in the range that it will work within. You will notice that it will stop at a certain point and won't focus past that spot (either near or far, depending). If it's focusing throughout the entire range, then it broke off in the "Full" setting, which is good because you can at least still use the lens. You (or the current owner) should consider getting that replaced/repaired unless you/they really don't use/care about that particular function.

It will still focus, but it depends upon which position the switch was in when it broke off. If it's on the "Limit" setting, it's going to be quite limited in the range that it will work within. You will notice that it stops at a certain point and won't focus past that spot (either near or far, depending). If it's focusing throughout the entire range, then it broke off in the "Full" setting, which is good for you because you can at least still use the lens. Since you didn't specify what is happening with your particular lens, I can only speculate that it's broken off at the "Full" setting. You should consider getting that replaced/repaired unless you really don't use/care about that particular function.