You put a rubber band on your cats wrist will it live?

If the rubber band wasn't tight, the cat likely simply kicked it off when it became annoying. If the rubber band was tight, the cat is likely to chew through it as soon as it becomes annoying. However, if the cat left the rubber band alone, and it was tight enough to cut off blood flow, eventually the rubber band would cause all the tissues (including the entire paw) below the rubber band to die and fall off. Depending upon the cat's overall health and exactly how the necrosis of the paw occurs, this could result in fatal blood poisoning.

I wouldn't suggest doing this to your cat - it's quite painful - but it's likely the cat would take care of the problem before it became life threatening.