If it appears to user as an "alert" to something they should "fix" or take special note of -- and it is specifically raised when your algorithm detects they are attempting to leave your website -- it is plainly deceitful.
If the alert says something untrue or misleading (last day of sale, virus on computer, 1000th visitor) that's deceitful.
Plus, it incentivizes having to threaten to cancel a deal to get anywhere near acceptable terms. Fuck that.
But basically off the page as regards to the specific UX patterns under discussion in this thread.
This one:
"when someone tried to leave the site, bring up a popup to offer them a deal or otherwise encourage them not to leave"
In other words: in the Venn diagram of the two buckets - the measure of overlap is quite small.