OK, so you are in the matrix hacking into someone's commlink. Bamm, there's an agent there which engages you in combat. You kick it's ass because that just what a super hacker like you would do...
What happens to the agent?

Does it just turn off and wait to be turned back on by the Sys Admin? Like in the next IP or Turn? (This would suck for the hacker to fight the same one over and over)
Does it get damaged and need the medic program used on it to become functionable again? (Hacker doesnt have to worry about the agent until well on down the line, and the owner still has his agent after repairs)
Does it just get destroyed, boom, bye bye, no more agent or programs loaded to it? (Keeps the shadow tech market moving and shaking, even without upgrades)

It doesnt specificly say in the BBB and the situation might arise where I might have to combat one soon.

the agent crashes, as i recall.

Off the cuff, I would say that the agent needs to be re-loaded. No real extra cost to the owner of that poor commlink, if he was smart enough to keep a copy (or more than one).

yeah they would probably go to a pay phone and report ID theft and get a new node to prevent it from happening.

I thought they just possessed another person near by, and starting beating you up again?