Got a voicemail claiming I was named in a civil suit and a process server would be after me soon. Where they overplayed their hand was telling me if I was not home they would deliver it to my employer who would then be responsible for serving the summons on me. Presumably that was meant to scare me into paying to settle a suit about which they gave no specifics.
The employer is not "responsible" at all, the server is. Court rules may allow that method. But then you would need to have a real lawsuit at issue, which you don't when some goon leaves a message warning you to be ready for process service. What you heard was all too typical of the bogus debt collector species.
FTC alert: "Fake Debt Collectors"
CFPB Q&A: Can a debt collector try to deceive me to collect on a debt?