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I'm not sure if this can be reproduced, but I used chronokeeper's ult on sivir at the exact moment of his death (I'm slow, yeah :P), and what appeared to happen was that he could run around at 0 health and would start slowly regening it. The problem was that nothing could "target" him. The towers wouldn't go after him, he soloed baron at ~12, he even attacked them at their fountain and nothing happened.
The second thing is that, you can target yourself with spells by clicking your portrait, unless you happen to level and have a skill point to put in.