I deleted my account on codegolf.stackexchange.com some time ago. The vast majority of my network reputation was derived from that site (I had approximately 20k rep when I deleted the account).
However, when I look at my account on chat.stackexchange.com, it's showing 22k reputation and six gold badges. These can only possibly have come from codegolf (I don't have nearly enough activity on other sites for that).
It seems like a major bug to retain this information; I can't see any good reason why a user should be credited for posts that they're no longer associated with. (It also concerns me that deleted accounts aren't being deleted "properly", e.g. I still have notifications from PPCG in my notifications list.) Note that part of the reason I deleted the account was to remove badges from it, and remove reputation from it without needing to use the disruptive method of continuously posting bounties, and as such I'm quite concerned that the reputation and bounties are still indirectly there.
Note also that it would probably be possible to use this mechanism to bypass the reputation cap; you could make a post, earn 200 reputation from it, delete your account on a particular site (as you still only have one post), create another account on the same site, earn another 200 reputation, and get a total of 400 "global" reputation. This would seem to violate the purpose of the reputation cap. (If this seems implausible – although in my experience, it's normally fairly easy to gain large amounts of reputation if you're merely aiming to gain reputation rather than to improve the site – consider instead the situation with bronze badges; you could create an account on a particular site, edit your profile to gain the badge, delete the account again, and repeat arbitrarily many times in order to gain arbitrarily many bronze badges.)
(See also this question, reporting a similar bug that affects the "can gain association bonuses" property of a global account, as opposed to the global badges and global reputation.)