It sounds like the string may have cut too far through the trunk for it to recover. A general rule is that a tree can usually survive if less than half its circumference is girdled. The half of the tree that was lacerated will not be able to transport water and nutrients up that half of the tree. This will lead to a slow decline of the tree. Bridge grafting can be used to save a girdled tree, but it sounds like this tree is too small to attempt that. If the cut was high up on the trunk, then you could prune out the top of the tree and hope it sends out new shoots from the lower half of the trunk. However, it may be easier to just replace it with a new tree.

It sounds like the string may have cut too far through the trunk for it to recover. A general rule is that a tree can usually survive if less than half its circumference is girdled. The half of the tree that was lacerated will not be able to transport water and nutrients up that half of the tree. This will lead to a slow decline of the tree. Bridge grafting can be used to save a girdled tree, but it sounds like this tree is too small to attempt that. If the cut was high up on the trunk, then you could prune out the top of the tree and hope it sends out new shoots from the lower half of the trunk or look for some suckers that you can train into a new tree. However, it may be easier to just replace it with a new tree.