The AI will carry on playing, but won’t attack you (unless a fleet was already on the way to your star). It will move ships around between stars in a way that almost, but not entirely, resembles defending itself. You should be able to defeat the AI easily. Use the defensive bonus to your advantage if you can.
A very important thing to know is that you can trade techs with the AI. If you send them a tech there is a very high chance they will send one back (if they have something you don’t). If they don’t send back then they probably don’t have enough money. If you’re desperate to get something from them then either wait until pay day or send the AI money before sending your tech gift.