It depends on whether or not someone "stayed on the line to be connected" to a real human after listening to the automated voice explain the issue and get sketchy. I think most of us hangup before that? I'd have to look back, I thought one person did hang on the line ... I can't remember and may be wrong...
My assumption is if you waited to be connected you'd divulge information (either through automated responses or with a human,) that will allow them to hijack your IP address or snake in so they can backdoor their software on your connected computers. You'd never realize it is there. Keyloggers, spyware, or trojans to name a few, and programs that scan your system for personal information to steal and misuse. It might not even be IP related, but was just to get your attention so that you will trust their bait and switch later. They also could be prepping you to get you to buy some IP protection (that doesn't really exist,) or maybe purchase a VPN from them. The fact that they said IP compromised leads me to believe they mean to get into your network or sell you something to soothe your fear.
Or, or if the automated voice continues after you hold for someone and tells you to press 1 for this and 2 for that, etc., pressing one of those numbers gives them permission to pester you in other multiple ways? Idk. I've never stayed on the line. I'm so sick of all companies and advertisers and surveys calling me several times a day, sometimes hourly, that I no longer pick up, or I hang up after hearing their first breath. The times I've waited long enough to tell them to remove me from their call list was so excruciatingly long and hair pulling and most don't readily say they will but instead try to get me to change my mind, or proceed to talk over me as if they didn't hear me. Some say very rude things to me. I don't have time in my day for that kind of time-wasting headache. I always say I'm reporting them. I once had a windows/siding company actually call me back and yell at me! They know ... they know. No one is going to come and make them stop.